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COMPARISON STUDY OF FUZZY C-MEANS AND FUZZY
SUBTRACTIVE CLUSTERING IMPLEMENTATION IN
QUALITY OF INDIHOME FIBER OPTIC NETWORK
(Case Study in PT. TELKOM INDONESIA)
THESIS
Submitted to International Program
Department of Industrial Engineering
as The Partial Requirement of Acquiring Bachelor’s Degree of Industrial
Engineering at Universitas Islam Indonesia
Name : Delia Isti Astari
Student No. : 14 522 166
INTERNATIONAL PROGRAM
DEPARTMENT OF INDUSTRIAL ENGINEERING
UNIVERSITAS ISLAM INDONESIA
YOGYAKARTA
2018
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DEDICATION
This thesis is dedicated for the one and only my mom, my dad, my brother, and all
my beloved family.
Thesis Supervisor,
Mr. Muhammad Ridwan Andi Purnomo, ST., M.Sc., PhD.
Best Friends and Industrial Engineering International Program UII Batch 2014
Family
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MOTTO
“Allah does not charge a soul except [with that within] its capacity. It will have
[the consequence of] what [good] it has gained, and it will bear [the consequence
of] what [evil] it has earned. "Our Lord, do not impose blame upon us if we have
forgotten or erred. Our Lord, and lay not upon us a burden like that which You
laid upon those before us. Our Lord, and burden us not with that which we have
no ability to bear. And pardon us; and forgive us; and have mercy upon us. You
are our protector, so give us victory over the disbelieving people.”
(Qur’an Surah (QS) Al Baqarah verse 286)
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PREFACE
Assalamualaikum warahmatullah wabarakatuh
Alhamdullillahirabbil'alamiin, praise the presence of Allah Almighty who has
delegated all his mercy and grace, so that the writer can complete this Thesis in
expected time accordance with Rasulullah SAW and his family, friends, and his
followers who have fought and guided us out of the darkness to the bright way to
reach the blessings of Allah SWT. Thanks to Allah SWT's grace, the thesis
entitled "Comparison Study of Fuzzy C-Means and Fuzzy Subtractive Clustering
Implementation for Quality of IndiHome Fiber Optic Network (Case Study in PT
Telkom Indonesia)" can be solved well. This thesis is arranged as one of the
requirements that must be fulfilled as The Partial Requirement of Acquiring
Bachelor’s Degree of Industrial Engineering at Universitas Islam Indonesia.
In completing the preparation of this thesis can not be finished from the
support, assistance, and guidance from various parties. For that the authors would
like to thank and reward the parties who have provided support directly or
indirectly, therefore with gratitude the authors thank to:
1. Both parents and all the big family member who always give prayers,
encouragement, and love to me.
2. Mr. Muhammad Ridwan Andi Purnomo, ST., M.Sc., Ph.D. who has guided and
provided solutions and suggestions in the completion of this thesis.
3. PT Telkom Indonesia branch Yogyakarta which has provided opportunities and
facilities that have facilitated the author in completing the Thesis.
4. Head of Laboratory, Laboran, and entire family of Laboratorium Statistika
Industri and Optimasi (SIOP) to my special bestfriend Citra, Feny, Dhaniya,
Febri, Adi and Alfiqra.
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5. Industrial Engineering International Program batch 2014 family and all those
who have prayed for, supported and motivated during the writing of the final
task that can not be mentioned one by one.
6. Mrs. Diana and Mrs. Devi that patiently help the students, especially the
author.
The Authors also thanks to all of concerned parties that cannot be
mentioned one by one who have helped the author in completing this report.
Hopefully, the goods which are given by all parties to the Author will be replied
by the kindness from Allah. Finally, the Author realizes that there are still
shortcomings as well as weaknesses in this report, so the building suggestions and
critics are fully expected. The author hopes this research would bring advantages
for everyone who reads this.
Wassalamu’alaikum Warahmatullah Wabarakatuh
Yogyakarta, August 2018
Delia Isti Astari
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ABSTRACT
This research is conducted for grouping or clustering the quality assessment rule
of IndiHome fiber optic cable network using fuzzy clustering method in PT
Telkom company and to understand the difference type of clustering by observing
the mapping and clustering data results that presented by each algorithm method
of Fuzzy Subtractive Clustering and Fuzzy C-Means Clustering results. It applied
ten predictor variables that affect the quality of the system through the study of
previous research literature. Several factors that affect the transmission are Tx
Power, Rx Power, Temperature, Power Supply, and Bias Current. Later, cluster
validation is performed by using Partition Coefficient Index (PCI) and Partition
Coefficient Index (PEI) indicator. This research uses the Fuzzy Subtractive
Clustering process with cluster radius is from 0.1 until 1. Each radius has each
number of clusters, nevertheless, for radius 0.1 the number of clusters that formed
are 4, while radius 0.2 to 1, there is only one cluster formed. In Fuzzy Subtractive
Clustering, it is considering some of the parameter which are the accept ratio 0.5,
the reject ratio 0.15, and squash factor 1.25. In Fuzzy C-Means result, the value of
the PCI (Partition Coefficient Index) is 0.662786731. Then, the value of the PEI
(Partition Entropy Index) is 0.546967522. From the results of Fuzzy Subtractive
Clustering, highest value of PCI are resulted in radius 1 with the value of
0.451738. The smallest PEI is in radius 0.2 with the value of 0. 0.070139. Then, it
can be stated that both methods are better within each parameter. But after
considering the number of clusters that are formed, compared to fuzzy c-means
method has 4 clusters and in fuzzy subtractive only two clustering numbers are
formed, which are 41 and 1. In conclusion, the method that will be preferred in
terms of grouping quality is Fuzzy C-Means.
Keywords: Quality, Fuzzy C-Means, Fuzzy Subtractive Clustering
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TABLE OF CONTENT
AUTHENTICITY STATEMENT.......................................................................... ii
THESIS APPROVAL OF SUPERVISOR ............................................................iii
THESIS APPROVAL OF EXAMINATION COMMITTEE ............................... iv
DEDICATION........................................................................................................ v
MOTTO ................................................................................................................ vi
PREFACE ............................................................................................................ vii
ABSTRACT............................................................................................................ix
TABLE OF CONTENT ......................................................................................... x
LIST OF TABLES ............................................................................................... xii
LIST OF FIGURES ............................................................................................ xiii
CHAPTER I INTRODUCTION ............................................................................ 1
1.1 Background ............................................................................................. 1
1.2 Problem Formulation .............................................................................. 4
1.3 Objectives of Research ............................................................................ 5
1.4 Scope of Problem .................................................................................... 5
1.5 Benefits of Research ................................................................................ 5
1.6 Systematical Writing ............................................................................... 6
CHAPTER II LITERATURE REVIEW ................................................................ 8
2.1 Deductive Study ......................................................................................... 8
2.1.1 Data Mining Concept ............................................................................. 8
2.1.2 Clustering Analysis .............................................................................. 11
2.1.3 Fuzzy Logic ......................................................................................... 14
2.1.4 Fuzzy Clustering .................................................................................. 17
2.2 Inductive Study ........................................................................................ 26
CHAPTER III RESEARCH METHODOLOGY ................................................ 34
3.1 Research Flowchart .................................................................................. 34
3.2 Problem Identification .............................................................................. 35
3.3 Problem Formulation................................................................................ 35
3.4 Literature Review ..................................................................................... 36
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3.5 Data Collection ......................................................................................... 36
3.6 Pre-Processing Data ................................................................................. 37
3.7 Data Processing ........................................................................................ 37
3.7.1 Fuzzy C-Means Processing ................................................................. 38
3.7.2 Fuzzy Subtractive Clustering Processing............................................ 38
3.8 Clustering Validation ............................................................................. 38
3.9 Discussion .............................................................................................. 39
3.10 Conclusion and Recommendation .......................................................... 39
CHAPTER IV DATA COLLECTING AND PROCESSING ............................. 40
4.1 Data Collection ......................................................................................... 40
4.2 Pre-Processing Data ................................................................................. 45
4.3 Data Processing ....................................................................................... 46
4.3.1 Fuzzy C-Means Processing ................................................................ 46
4.3.2 Fuzzy C-Means Validation.................................................................. 55
4.3.3 Fuzzy Subtractive Clustering Processing............................................ 58
4.3.4 Fuzzy Subtractive Clustering Validation............................................ 73
CHAPTER V DISCUSSION .............................................................................. 77
5.1 Grouping System Quality with Fuzzy C-Means Method ........................ 77
5.2 Grouping System Quality with Fuzzy Subtractive Clustering Method ... 79
5.3 Sensitivity Analysis on Fuzzy Subtractive Clustering ............................. 81
CHAPTER VI CONCLUSION AND RECOMMENDATION .......................... 84
6.1 Conclusion ............................................................................................... 84
6.2 Recommendation ...................................................................................... 85
6.2.1 For PT Telkom Indonesia branch Yogyakarta.................................... 85
6.2.2 For Further Researchers....................................................................... 85
REFFERENCES ................................................................................................. 86
APPENDICES .................................................................................................... 90
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LIST OF TABLES
Table 1.1 Competition Map of Local and Foreign Telecommunication Industry in
Indonesia................................................................................................................. 2
Table 2.1 Inductive Study..................................................................................... 31
Table 4.1 Data Recapitulation IndiHome System................................................. 41
Table 4.2 Degree of Membership.......................................................................... 49
Table 4.3 Clustering Result................................................................................... 50
Table 4.4 PCI Result on Fuzzy C-Means.............................................................. 55
Table 4.5 PEI Result on Fuzzy C-Means.............................................................. 57
Table 4.6 Normalization Data............................................................................... 60
Table 4.7 Initial Potential...................................................................................... 65
Table 4.8 New Potential........................................................................................ 67
Table 4.9 Normalization and Denormalization Data............................................ 70
Table 4.10 Sigma Cluster...................................................................................... 71
Table 4.11 Degree of Membership using Radius 0.2............................................ 72
Table 4.12 PCI Result on Fuzzy Subtractive Clustering....................................... 73
Table 4.13 PEI Result on Fuzzy Subtractive Clustering....................................... 75
Table 5.1 Number of Cluster................................................................................. 80
Table 5.2 PCI and PEI value................................................................................. 82
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LIST OF FIGURES
Figure 2.1 KDD Process......................................................................................... 9
Figure 2.2 Fuzzy Logic......................................................................................... 15
Figure 2.3 Gauss Curve Membership Function.................................................... 24
Figure 3.1 Research Flowchart............................................................................. 34
Figure 4.1 Relationship between Objective Function with the Number of
Iterations ............................................................................................................. 48
Figure 4.2 Data Plot for Each Cluster in 4 Clusters.............................................. 54
Figure 5.1 Sensitivity Analysis based on PCI and PEI......................................... 82
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CHAPTER I
INTRODUCTION
1.1 Background
It is important to consider that the processes and operations are often linked via process
intra- and inter-relations to each other and thus, the variations can, even being tolerable
from an individual (isolated) process perspective, lead to an unacceptable accumulation
causing failure of the final product to meet the customer requirements (Wuest et al.
2013). An important things is the quality by both producers and consumers so it has a
very important meaning for the survival of business activities in the field of services and
manufacturing. Quality has become a demand of society in the era of global
competition. Maintaining quality is important because; it can reduce costs. Companies
by harvesting technological innovations can provide high quality and personalized
service at reasonable costs (Rust & Miu, 2006). Companies that make quality as a
strategy tool will have the advantage to compete against its competitors in the market
because not all companies can achieve the superiority of quality. In this case the
company is required to produce products with high quality, low price and timely
delivery.
Under conditions of intense competition among telecommunication service
providers, companies are required to improve the quality of services and products
produced. With more choices in the market, consumers have a higher bargaining power
in choosing products according to their needs. The competition in telecommunication
industry in Indonesia is increasingly tight, in addition to competition among local
telecommunication companies is also enlivened by the increasing number of foreign
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telecommunications companies entering Indonesia, where in general the area of
competition is done with a variety of bonus facilities, cheap tariffs, and product
differentiation offered (Wiryono & Suharto, 2008). This can be seen in Table 1.1.
Nevertheless, each telecommunication service provider strives to concentrate on
expanding the market.
Table 1.1 Competition Map of Local and Foreign Telecommunication Industry in
Indonesia
Company Tech License
Telkomsel
GSM & 3G
Nation wide
Indosat
Excel
Natrindo GSM
Regional
CAC Not Operated Yet
Telkom
CDMA (Fixed Wireless)
Nation wide
Mobile-8
Bakrie Tel Regional
Telkom Fixed Wireline
Nation wide
BBT Limited Area
Sampoerna Tel NMT-450 Regional
Source: (Wiryono & Suharto, 2008)
This research was conducted in PT. Telekomunikasi Indonesia Tbk which is one
of the SOEs whose currently owned by the Government of Indonesia (52.56%), and
47.44% is owned by the Public, Bank of New York and Domestic Investors. PT.
Telekomunikasi Indonesia Tbk, which is now better known as Telkom Group is the
only State-Owned Enterprises telecommunication company and the largest
telecommunication and network service provider in Indonesia. PT Telkom Indonesia
with Speedy products that now changed to Indonesia Home (IndiHome) is the largest
internet service provider in Indonesia, with relatively cheap for its monthly cost, this
internet service is used by many customers all over Indonesia. For the IndiHome service
using fiber optic, sometimes, issues will happen such as network break or the network
becomes slow. Occasionally, customers complain about the presence of interruptions
and a sudden drop in speed. The company will perform controlling and maintenance
only when the customer propose the complaints. The company unaware on know the
quality of the system for each customer. The company also unspecify the quality that
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should be understood by its employees that leads to the lack of preparedness to respond
the complain on time.
Based on these problems, this research is conducted for grouping or clustering the
quality system of IndiHome fiber optic cable network using fuzzy clustering method in
PT Telkom company and to compare the prediction result or to evaluate the
performance obtained by Fuzzy Subtractive Clustering and Fuzzy C-Means Clustering
results. Clustering is one of the data mining functions that is used to group data into a
class or cluster, so that objects on a cluster have a very large similarity with other
objects on the same cluster, but it is very similar to other cluster objects (Tan,
Steinbach, Karpatne, & Kumar, 2013). Fuzzy clustering techniques allow the automatic
generation of fuzzy models and can be utilized to predict the quality. In fact, fuzzy
modeling means more flexible modeling-by extending a zero-one membership in the
interval (0.1), can be said to be more flexible (Takagi & Sugeno, 1985). Then using
fuzzy modeling is simplifying the formulation of the problem as it reduces the cost of
computing. This is due to the fact that the non-fuzzy (generally crisp) model generally
produces a complete search in large space (since some key variables can only take
values 0 and 1), whereas in the fuzzy model all variables are continuous, so the
derivative can be calculated to find the direction for the search (Gorrostieta, Pedraza, &
Carlos, 2005).
Finally fuzzy modeling can be an automated or semi-automated process using
grouping techniques such as Fuzzy C-means Clustering (FCM) and Fuzzy Subtractive
Clustering (FSC) (Yager & Filev, 1994). In this research, the data did not use the class
label so therefore it is categorized as an unsupervised method. Where, for Fuzzy C-
Means is an unsupervised method and Fuzzy Subtractive Clustering is a supervised
method and each cluster center can be used as a rule base that describes system
behavior. For fuzzy subtractive clustering also can be said as an unsupervised method.
According to Yaqin, et al. (2018), fuzzy subtractive clustering method relatively
unsupervised clustering method in which the number of cluster centers is unknown.
Implementation of data mining algorithm using Fuzzy Subtractive Clustering and Fuzzy
C-Means when being viewed from some previous researches can provide the best
clustering data by some parameter. Both models have significant results and also have
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some differences in the shape and pattern of the cluster. Therefore a comparison test
between two methods of data mining on both modeling is made to understand the
different type of clustering. Particularly, for designated case study in analyzing the
Quality of IndiHome Fiber Optic Network by considering the mapping and clustering
data results from the clustering presented by each algorithm method.
At the same time, the sensitivity analysis is important to do in Fuzzy Subtractive
Clustering with the range 0 – 1 because the output which produced by the different
radius will have the variation in results. From the result, it can be seen that varying the
cluster radius will obtain the different outputs. Analysis should be performed to
examine the sensitivity due to the uncertainties result. FSC has an inconsistency
problem where different way in running the FSC yields different results. Bataineh,
Nadji & Saqer (2011) conducted the comparison for both methods was based on the
validity measurement of their clustering method. The effects of different parameters on
the performance of the algorithms are investigated. The parameter of validity
measurement is Partition Coefficient Index (PCI) and Partition Entropy Index (PEI).
Highly non-linear functions are modeled and a comparison is made between the two
algorithms according to their capabilities of modeling. The number of clusters for the
fuzzy c-mean algorithm is determined. The validity results are calculated for several
cases. As for fuzzy subtractive clustering, the radius parameter is changed to obtain a
different number of clusters. Generally, increasing the number of generated clusters
yields an improvement in the validity index value. The optimal modeling results are
obtained when the validity indices are on their optimal values.
1.2 Problem Formulation
Based on the background of research elaborated above, the problem formulation in this
research are:
1. What is the result of the cluster validity performance value with the Partition
Coefficient Index (PCI) and Partition Entropy Index (PEI) indicator produced by
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Fuzzy C-Means and Fuzzy Subtractive Clustering in clustering the IndiHome
quality system?
2. How is the sensitivity from testing the influence of a radius of 0.1 to 1 in the
Fuzzy Subtractive Clustering method used in clustering the IndiHome quality
system?
1.3 Objective of Research
In this section, the objectives in creating this research are revealed, as follows:
1. To identify the result of the validity performance value with the Partition
Coefficient Index (PCI) and Partition Coefficient Index (PEI) indicator
produced by Fuzzy C-Means and Fuzzy Subtractive Clustering in clustering the
IndiHome quality system.
2. To find out how the sensitivity testing the influence of radius of 0.1 to 1 in the
Fuzzy Subtractive Clustering method used in clustering the IndiHome quality
system.
1.4 Scope of Problem
There are several limitations that existed in this research, as mentioned as follows:
1. The data used in quality measurement only a few variables.
2. This research did not examine the fuzzy clustering in depth until to get the final
IF-THEN rule result.
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1.5 Benefit of Research
The following are the benefits of this research:
1. The company can produce quality groupings so that they will be able to make
different treatment from each cluster.
2. Comparative results can be used to see the performance differences of the Fuzzy
Subtractive Clustering and Fuzzy C-Means Clustering methods.
1.6 Systematical Writing
The systematical writing in this study are:
CHAPTER I INTRODUCTION
This chapter explains the introduction of the research. In this
chapter, there will be elaborated the problem background,
problem formulation, research objective, scope of the problem,
research benefit, and systematical writing.
CHAPTER II LITERATURE REVIEW
This chapter focuses to determine the current study of the related
previous researches by finding the state of the art of the previous
researches to make difference with other researches. In this
chapter, there will be elaboration between inductive and
deductive studies related to the topic. The chapter contains
information about the result of related previous research and
supporting literature underlying the research.
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CHAPTER III RESEARCH METHODOLOGY
This chapter will describe the research methodology. In this
chapter, there will be described the detailed series of research
object, research flow, and method used for the research including
data collecting, data processing, and analyzing method.
CHAPTER IV DATA COLLECTING AND PROCESSING
This chapter describes the data collection and processing, analysis
and results, including images, graphics, and tables obtained. In
addition, this chapter also explains thoroughly about the data
processed using the aforesaid method. This chapter is a reference
for the discussion of the results that will be written in Chapter V.
CHAPTER V DISCUSSION
This chapter contains the analysis about the result of the previous
chapter. In this chapter, core discussion will be conducted in order
to get a comprehensive understanding of the whole research.
CHAPTER VI CONCLUSION AND SUGGESTION
This chapter provides short and precise statements described in
the previous chapter which answer the problem formulation of the
research. Suggestion related to the current study in the purpose of
the advancement of the future research is given based on the
limitations of the current research.
REFERENCES
APPENDIX
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CHAPTER II
LITERATURE REVIEW
2.1 Deductive Study
2.1.1 Data Mining Concept
Data Mining is a series of processes to explore the added value of information that
has not been known manually from a database by extracting patterns from the data in
order to manipulate data into more valuable information obtained by extracting and
recognizing important patterns or pulling from the data contained in the database.
Due to the wide variety of Data Mining techniques and many different types of
information and forms of data presentation, it is necessary to define the limits of the
applicability and relevance of certain methods according to the provided data and the
achieved objectives. It is also necessary to understand how the problem should be
solved with the Data Mining south as classification, regression, clustering and so on
(Vadim, 2018). The main reason why data mining has attracted the attention of the
information industry in recent years is because of the availability of large amounts of
data and the increasing need for transforming the data into useful information and
knowledge as it focussed on the field of science that is doing extracting or mining
activities of the data size / large quantities, this information that will be very useful
for development.
Data mining is also known by other names such as Knowledge discovery
(mining) in databases (KDD), knowledge extraction, data analysis and business
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intelligence and is an important tool for manipulating data for presenting information
as needed users with the aim to assist in the analysis of behavioral observation
collections, in general the definition of data-mining can be interpreted as follows:
The process of finding interesting patterns from large amounts of stored data.
The extraction of useful or interesting information (non-trivial, implicit, as
yet unknown potential use) pattern or knowledge of data stored in large sums.
Exploration of automated or semi-automatic analysis of large amounts of data
to search for meaningful patterns and rules.
Figure 2.1 below shows the process of Knowledge Discovery in Database. The
phases of the process are as follows:
Figure 1.1 KDD Process
Source: Vannozzi, Croce, Starita, Benvenuti, & Cappozzo (2004)
1. Selection
Creating a target data set, selecting a data set, or focusing on a subset of
variables or sample data, where discovery will be performed.
Data selection from a set of operational data needs to be done before the stage
of extracting information in KDD begins. Selected data will be used for the
data mining process, stored in a file, separate from the operational database.
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2. Pre-processing
Preliminary processing and data cleaning are basic operations such as noise
removal.
Before the data mining process can be implemented, it is necessary to do the
cleaning process on the data that became the focus of KDD.
The cleaning process includes removing data duplication, checking
inconsistent data, and correcting data errors, such as typographical errors.
Enrichment process is carried out, ie the process of existing data with other
relevant data or information required for KDD, such as external data or
information.
3. Transformation
The search for useful features for presenting the data depends on the goal to
be achieved.
A process of transformation on the data that has been selected, so the data is
appropriate for the process of data mining. This process is a creative process
and depends on the type or pattern of information to be searched in the
database.
4. Data mining
Selection of data mining tasks; the selection of goals from the KDD process
such as classification, regression, clustering, etc.
Selection of data mining algorithm for searching.
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Data Mining process is the process of finding patterns or interesting
information in selected data using a particular technique or method.
Techniques, methods, or algorithms in data mining vary widely. The choice
of the appropriate method or algorithm depends heavily on the purpose and
process of KDD as a whole.
5. Interpretation / Evaluation
Translation of patterns resulting from data mining.
The pattern of information generated from the data mining process needs to
be displayed in a form that is easily understood by interested parties.
This stage is part of the KDD process that includes examining whether the
pattern or information found is contrary to previous facts or hypotheses.
2.1.2 Clustering Analysis
A.1 Introduction
Clustering refers to the process of grouping samples so that the samples are similar
within each group (Gose, Johnsonbaugh, & Jost, 2018). Clustering can be considered
the most important unsupervised learning problem; so, as every other problem of this
kind, it deals with finding a structure in a collection of unlabeled data. An example
where this might be used is in the field of psychiatry, where the characterization of
patients on the basis of clusters of symptoms can be useful in the identification of an
appropriate form of therapy. In marketing, it may be useful to identify distinct groups
of potential customers so that, for example, advertising can be appropriately
targetted. Benefits of Clustering is a method of data segmentation that is very useful
in predicting and analyzing certain business problems. For example market
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segmentation, marketing, and territorial mapping. Furthermore, the identification of
objects in fields such as computer vision and image processing.
A good clustering will result in a high degree of commonality in one class and
a low degree of commonality between classes. The similarity is a numerical
measurement of two objects. The value of similarity between the two objects will be
higher if the two objects are compared have a high similarity. The quality of
clustering results depends on the method used. In clustering known four data types.
The four data types are:
Interval-scale variable
Binary variables
The nominal, ordinal, and ratio variables
Variables with other types.
The clustering method should also be able to measure its own ability in an
attempt to find a hidden pattern on the data under study. There are various methods
that can be used to measure the value of similarity between the objects that are
compared. One of them is the weighted Euclidean Distance. Euclidean distance
calculates the distance of two points by knowing the value of each attribute on both
points. Here's the formula used to calculate the distance with Euclidean distance in
Equation 2.1:
... (2.1)
Where:
n = Total of record data
k = Sequence of data fields
r = 2
µk = Weight field given a user
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Distance is a common approach used to determine the similarity or inequality
of two feature vectors expressed by rank. If the value of the resulting rank the
smaller the value the closer or higher similarity between the two vectors. Distance
measurement techniques with the Euclidean method become one of the most
commonly used methods. Distance measurement with the euclidean method can be
written in the Equation 2.2:
... (2.2)
where v1 and v2 are two vectors whose distance will be calculated and N denotes the
length of the vector.
A.2 Clustering Procedures
1. Non-hierarchical clustering (also called k-means clustering)
In this analysis, k number of clusters is chosen. Each of these clusters is assigned a
centroid (or center). These initial centroids can be taken randomly, but it is
important for researchers to recognize that different locations of the centroids can
cause different results. Next, we determine the distance of each object to the nearest
centroid. Then, we need to recalculate new centroids, which result from the clusters
of the previous step. After we have these new centroids, we have to bind the points
again to their nearest centroid. We group each object by a minimum distance to the
centroid and continue doing so until we find convergence and stability (i.e. centroids
do not move anymore). The goal of k-means cluster analysis is to minimize the
summed distance between all data points and the cluster centroids. The diagram to
the right explains the procedure. This process does not always find the optimal
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configuration and results can be easily affected by randomly selected centroids.
Outliers may also have a strong effect on results.
2. Hierarchical clustering
In hierarchical clustering, objects are organized into a hierarchical structure as part of
the procedure. We start with n total points and clusters each containing a single point
(n total clusters). Then we look for the closest two clusters (using one of several
distance measures explained above). This leaves us with n-1 total clusters, with all
but one containing a single element. We continue this process using the distance
between cluster centroids. This agglomerative process uses a “bottom-up” strategy
to cluster single elements into successively larger clusters. There are several methods
for agglomerative clustering, including:
a. Centroid methods mean clusters are generated that maximize the distance between
the centers of clusters (a centroid is a mean value for all the objects in the cluster).
b. Variance methods mean clusters are generated that minimize the within-cluster
variance.
c. Ward’s Procedure means clusters are generated that minimize the squared
Euclidean distance to the center mean.
d. Linkage methods mean objects are clustered based on the distance between them.
2.1.3 Fuzzy Logic
Since 1985 when the fuzzy model methodology suggested by Takagi-Sugeno
(Takagi & Sugeno, Fuzzy Identification of Systems and its Application to Modeling
and Control, 1985), as well known as the TSK model, has been widely applied on
theoretical analysis, control applications and fuzzy modeling. The fuzzy system
needs the antecedent and consequence to express the logical connection between the
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input-data and output-data that is used as a basis to produce the desired system
behavior (Sin & De, 1993). Fuzzy Logic is a troubleshooting methodology with
thousands of applications in stored controls and information processing. Suitable to
be implemented on a simple, small, embedded system on a microcontroller, multi-
channel PC or workstation based data acquisition and control system. Figure 2.2
shows that the fuzzy logic provides a simple way to describe the exact conclusions of
information that is ambiguous, vague, or incorrect. In a sense, fuzzy logic resembles
human decision making with its ability to work from interpreted data and find the
right solution.
Figure 2.2 Fuzzy Logic
Source: Puspita & Yulianti (2016)
Fuzzy logic is basically a logical value that can define values between
conventional states like yes or no, true or false, black or white, and so on. Fuzzy
reasoning provides a way to understand the performance of the system by assessing
the input and output system of observations. To do the design of a fuzzy system
needs to do some of the following stages:
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a. Defines model characteristics functionally and operationally.
In this section to note what characteristics of existing systems, then formulated the
characteristics of operations that will be used on the fuzzy model.
b. Decomposition of model variables into fuzzy sets
From the variables that have been formulated, formed related fuzzy sets without
overriding the domain.
c. Creating fuzzy rules
The rules on a fuzzy show how a system operates. The way of writing rules in
general is: If (X1 is A1). .... (Xa is An) Then Y is B with (.) Is operator (OR or
AND), X is scalar and A is linguistic variable.
Things to consider in creating rules are:
Grouping all rules that have solutions on the same variable.
Sorting rules for easy reading.
Using an identity to show the rule structure.
Using common naming to identify variables in different classes.
Using comments to describe the purpose of a or a group of rules.
Providing spaces between rules.
Writing variable with big letters, fuzzy set with capital letters and other
language elements with lowercase letters.
d. Define the defuzzy method for each solution variable
In the defuzzy stage, a value of a solution variable which is consequently selected
from the fuzzy region is selected. The most commonly used method is the centroid
method, this method has a high consistency, has a high and total width of a
sensitive fuzzy area.
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2.1.4 Fuzzy Clustering
A.1 Definition
Traditional clustering approaches generate partitions; in a partition, each instance
belongs to one and only one cluster. Hence, the clusters in a hard clustering are
disjointed. Fuzzy clustering, for instance, extends this notion and suggests a soft
clustering schema. In this case, each pattern is associated with every cluster using
some sort of membership function, namely, each cluster is a fuzzy set of all the
patterns. Larger membership values indicate higher confidence in the assignment of
the pattern to the cluster. The purpose of clustering is to identify natural groupings of
data from a large data set to produce a concise representation of a system's behavior.
A hard clustering can be obtained from a fuzzy partition by using a threshold of the
membership value. The results of traditional clustering approaches are not
appropriate to define clusters as modules in product design. Fuzzy clustering
approaches can use fuzziness related to product design features and provide more
useful solutions. Measuring result processing is proposed to be performed with a
cluster analysis method enabling division of pooled data under consideration into
groups of similar objects (clusters) and record distribution into different groups or
segments.
Most clustering algorithms may be used under conditions of almost the whole
unavailability of information on data distribution laws. Objects with quantitative
(numerical), qualitative or mixed attributes are subject to clustering. Division of
sampled information into groups of similar objects simplifies further data processing
and decision-making as a specific analysis method may be used for each cluster. The
clustering algorithm is the a function: X->Y that assigns to all x€X objects numbers
of y€Y clusters. The Y range is known in advance in some cases but normally the
objective is to determine an optimum cluster number in terms of the specified
criterion of clustering quality. Membership grades are assigned to each of the data
points. These membership grades indicate the degree to which data points belong to
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each cluster. Thus, points on the edge of a cluster, with lower membership grades,
may be in the cluster to a lesser degree than points in the center of a cluster.
A.2 Fuzzy Clustering Algorithm Method
The different fuzzy clustering methods are described as follows.
1. Fuzzy C-Means Clustering Method
The most popular fuzzy clustering algorithm is the fuzzy c-means (FCM)
algorithm. Even though it is better than the hard K-means algorithm at avoiding
local minima, FCM can still converge to local minima of the squared error
criterion (Elmzabi, Bellafkih, Ramdani, & Zeitouni, 2004). The fuzzy c-means
algorithm attempts to partition a finite collection of elements X={ x1,x2,...,xn}
into a collection of c fuzzy clusters with respect to some given criterions. Fuzzy
sets allow for degrees of membership. A single point can have partial
membership in more than one class.
There can be no empty classes and no class that contains no data points.
The output of such algorithms is a clustering, but not a partition sometimes
(Nugraheni, 2013). This algorithm, data are a leap to every cluster by
membership procedure, which represents the fuzzy performance of algorithms.
The algorithm constructs a suitable matrix named U, factors are numbers
between 0 and 1 also represent the level of membership among data and centers
of clusters.
According to Gusti (2012), the earliest stages of Fuzzy C-Means concept
were to determine the center of the cluster (centroid) that would identify the
average location or space for each cluster. In the initial conditions, the center of
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this cluster cannot be accurately said this is caused by each data has a degree of
membership for each cluster. Improvements to the central cluster (centroid) and
each of the data values by repetition, it will be seen that the center of the cluster
(centroid) will move closer to the correct space/location.
Based on the minimization of the rational function that represents the
distance given to the centroid or cluster center of the data points by repairing the
centroid and the membership value of each data repetitive or repetitive, the exact
center position of the cluster (centroid) can be found. Fuzzy C-Means modeling
stages from the beginning of the algorithm start as determining each cluster
number, initial objective function, initial iteration, maximum iteration, rank,
smallest expected error, generate random numbers, calculate the sum of each
column and then calculate the center the kth cluster to produce the final data
clustering. The output generated from Fuzzy C-Means (FCM) is a row of cluster
centers and some degree of membership for each data point.
In this research, the development of a prediction model on Fuzzy C-Means
Clustering method is done in 7 stages. The following is the development stage of
the prediction model using the Fuzzy C-Means method (Prihatini, 2015):
1. Input data to be grouped, ie X is a matrix of size n x m (n = number of data
samples, m = attribute of each data). Xij the sample data to-i (i = 1,2, ...., N),
j-attribute (j = 1,2, ..., m).
2. Determine:
a. the number of clusters (c)
b. ranks for the partition matrix (w)
c. maximum iteration (maxIter)
d. least expected error (ξ)
e. initial objective function (Po = 0)
f. and initial iteration (t = 1).
3. Generate random numbers μik, i = 1,2, ..., n; k = 1,2, ..., c as elements of the
initial partition matrix U.
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4. Calculate the center of the k-cluster: Vkj, with k = 1,2, ..., c; and j = 1,2, ..., m,
using Equation 2.3 (Yan, Ryan, & Power, 1994):
... (2.3)
with:
Vkj = center of k-cluster for j-attribute
µik = degree of membership for i-th sample data at the k-th cluster
Xij = i-data, j-attribute
5. Compute the objective function on the t iteration using Equation 2.4 (Yan,
Ryan, & Power, 1994):
... (2.4)
with:
Vkj = center of cluster to k for attribute to j
µik = degree of membership for sample data to i on the k-th cluster
Xij = i-data, j-attribute
Pt = objective function on the t iteration
6. Calculate the partition matrix change using Equation 2.5 (Yan, Ryan, &
Power, 1994):
... (2.5)
with i = 1,2, ..., n; and k = 1,2, ..., c
Where :
Vkj = center of cluster to k for attribute to j
Xij = data to i, attribute to j
µik = degree of membership for sample data to i on cluster to k
7. Check stop condition:
If: (|Pt – Pt-1|< ξ or (t > MaxIter) then stop. If not: t = t +1, repeat step 4.
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2. Fuzzy Subtractive Clustering Method
Clustering algorithms typically require the user to pre-specify the number of
cluster centers and their initial locations. Estimated number and initial location
of cluster centers in simple and effective algorithm is called as the mountain
method. The method is based on gridding the data space and computing a
potential value for each grid point based on its distances to the actual data points.
A grid point with many data points nearby will have a high potential value. The
grid point with the highest potential value is chosen as the first cluster center.
The key idea in their method is that once the first cluster center is chosen, the
potential of all grid points is reduced according to their distance from the cluster
center. Grid points near the first cluster center will have greatly reduced
potential. The next cluster center is then placed at the grid point with the highest
remaining potential value. This procedure of acquiring new cluster center and
reducing the potential of surrounding grid points repeats until the potential of all
grid points falls below a threshold.
According to Chiu (1994), it uses data points as the candidates for cluster
centers, instead of grid points as in mountain clustering. The computation for
this technique is now proportional to the problem size instead of the problem
dimension. The problem with this method is that sometimes the actual cluster
centres are not necessarily located at one of the data points. However, this
method provides a good approximation, especially with the reduced computation
that this method offers. It also eliminates the need to specify a grid resolution, in
which tradeoffs between accuracy and computational complexity must be
considered. The subtractive clustering method also extends the mountain
method’s criterion for accepting and rejecting cluster centres. Although the
Subtractive Clustering is fast, robust and accurate, the user-specified parameter
(the radius of influence of cluster center) in this method, strongly affects the
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number of rules generated. A large generally results in fewer rules, while a small
can produce immoderate number of clusters.
In the implementation, it can be used 2 fractions as a comparator factor,
that is accept ratio and reject ratio. The accept ratio is the lower limit at which a
point the data being candidate (candidate) cluster center is allowed to become
the center of the cluster. While the reject ratio is the upper limit in which a data
point becomes a candidate (candidate) cluster center is not allowed to become
the center of the cluster. At an iteration, if it has been found a data point with the
highest potential, then it will be continued by searching the potential ratio of that
data point with the highest potential of a data point at the beginning of the
iteration. For the development of prediction model on Fuzzy Subtractive
Clustering method is done in 7 stages. The following is the development stage of
the prediction model using the Fuzzy Subtractive method (Kusumadewi &
Purnomo, 2013):
1. Input data to be clustered: Xij, with i = 1,2, ... n; and j = 1,2, ... m.
2. Set value:
a. rj (the radius of each data attribute); j = 1,2, ... m;
b. q (squash factor);
c. accept_ratio
d. reject_ratio;
e. XMin (minimum data allowed)
f. XMax (maximum data allowed)
3. Normalization
Calculate the normalization using Equation 2.6:
Xij =
... (2.6)
i = 1,2, ..., n; j = 1,2, ..., m
4. Determine the initial potential of each data point
a. i = 1
b. Do it up to i = n,
1.) Tj = Xij; j = 1,2, ..., m (2)
2.) Calculate the Distkj based on Equation 2.7:
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Distkj = (
) ... (2.7)
j = 1,2,....,m; k = 1,2,....n
3.) Initial potential
If m = 1, then follow the Equation 2.8:
Di = ... (2.8)
If m > 1, then follow the Equation 2.9:
... (2.9)
4.) i = i + 1
5. Find the point with the highest potential
a. M = max [In | i = 1,2, ..., n];
b. h = i, such that Di = M;
6. Determine the cluster center and reduce its potential to the surrounding points.
a. Center = []
b. Vj = Xhj; j = 1,2, ..., m;
c. C = 0 (number of clusters);
d. Condition = 1;
e. Z = M;
f. Do if (condition ≠ 0) and (Z ≠ 0):
1) Condition = 0 (there is no new center candidate yet);
2) Ratio = Z / M
3) If ratio> acceptance ratio, then condition = 1; (there is a new center
candidate)
4) If not then the ratio> refusal ratio, (a new center candidate will be
accepted as the center if its existence will provide balance to the data that
is located far enough with the existing cluster center)
7. Return the cluster center from the normalized shape to the original shape.
Centerij = Centerij * (XMaxj - Xminj) + XMinj; ... (2.10)
8. Calculate the sigma value of the cluster using Equation 2.11:
j = rj * (
√ ) ... (2.11)
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The result of this algorithm is the sigma value ( used to determine the
parameter value of the fuzzy membership function. In this study used Gauss
membership function as seen in Figure 2.3.
Figure 2.3 Gauss Curve Membership Function
Source: Fat (2014)
With the Gauss curve the membership degree of a data xi in k-group is in
Equation 2.12:
... (2.12)
From the description above can be seen that FSC has 4 parameters that are
radius cluster, with upper acceptance limit and lower rejection limits and squash
factor. These four parameters will affect the number of rules and error size
(Kusumadewi, 2002).
a) Squash factor is used to multiply the radius value, in determining the center of
the nearby cluster where its existence against the other center of the cluster
will be reduced (default = 1.25).
b) Accept ratio is used to set the potential of each member to be the center of the
cluster. If a member has a potential above the accept ratio then expected to be
a cluster center (default = 0.5).
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c) Reject ratio is used to set the potential of each member to be the center of the
cluster. If any member has a potential under the reject ratio then the member
will never be a cluster center (default = 0.15).
d) The cluster radius is used as the distance to be used in forming group
members from each cluster. The higher the radius value then the number of
clusters will be lesser, and dominant will generate a high error value.
A.3 Clustering Validation
Cluster analysis aims at identifying groups of similar objects and, therefore helps to
discover distribution of patterns and interesting correlations in large data sets. However,
it is a difficult problem, which combines concepts of diverse scientific fields (such as
databases, machine learning, pattern recognition, statistics). Thus, the differences in
assumptions and context among different research communities caused a number of
clustering methodologies and algorithms to be defined (Halkidi, Batistakis, &
Vazirgiannis, 2001). Validation includes efforts by the researcher to ensure that the
cluster results are representative of the population in general and thus can be
generalized to other objects and stable for a certain time.
Type of clustering validation are:
1. Partition Coefficient Index (PCI)
Bezdek (1981) proposes validity by calculating the partition coefficient (PC) as an
evaluation of the value of data membership in each cluster. The PC Index value (PCI)
only evaluates the degree of membership, regardless of the vector (data) value that
usually contains geometric information (data distribution). The value of PCI is said to
be able to measure the amount of overlapping between groups. The value in the range
[0,1], the larger value (close to 1) means that the cluster quality is getting better. Here's
the formula for calculating PC Index using Equation 2.13:
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PCI=
∑ ∑
... (2.13)
Where 𝑁 represents the amount of data in the data set, 𝐾 represents the number of
clusters, whereas 𝑢 denotes the membership value of the i data of the j-cluster.
2. Partition Entropy Index (PEI)
The partition entropy (PE) index is another fuzzy validity index that involves only the
membership values. It is defined as Bezdek (1981) in Equation 2.14:
PEI = -
∑ ∑
... (2.14)
Where a is the base of the logarithm and U = (µli) is the membership matrix of a
fuzzy c-partition. The values of the PE index range in [0, loga c]. The closer the value of
PEI to 0, the harder the clustering is. The values of PEI close to the upper bound
indicate the absence of any clustering structure inherent in the data set of the inability of
the algorithm to extract it. The PE index has the same drawbacks as the PC index.
2.2 Inductive Study
Fuzzy clustering is especially useful for fuzzy modeling especially in identifying fuzzy
rules. Research on the application of Fuzzy Clustering method conducted by Ferarro &
Giordani (2017) modifies fuzzy k-means clustering method for LR fuzzy data (PFkM-
F). This paper focuses on robust clustering of data affected by imprecision. The
clustering process is based on the fuzzy and possibilistic approaches. This has been
done by a comparing the performance of PFkM-F with the ones of other related
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clustering methods for fuzzy data. The researchers have found that PFkM-F worked in a
satisfactory way also in comparison with its competitors.
Other studies that apply the Fuzzy Clustering method are done by Zhu, Pedrycz,
& Li (2017) using Particle Swarm Optimization (PSO) and Fuzzy K-Means. Two data
transformation methods are proposed, Particle Swarm Optimization (PSO) is used to
determine the optimal transformation realized on a basis of a certain performance index.
Experimental studies completed for a synthetic data set and a number of data sets
coming from the Machine Learning Repository demonstrate the performance of the
FCM with transformed data. The experiments show that the proposed fuzzy clustering
method achieves better performance (in terms of the clustering accuracy and the
reconstruction error) in comparison with the outcomes produced by the generic version
of the FCM algorithm.
Research by using Fuzzy Subtractive Clustering method by researcher Marzouk
& Alaraby (2012) presented a fuzzy subtractive modelling technique to predict the
weight of telecommunication towers which was used to estimate their respective costs.
The towers considering four input parameters: tower height; allowed tilt or deflection;
antenna subjected area loading; and wind load. Telecommunication towers were
classified according to designated code (TIA-222-F and TIA-222-G standards) and
structures type (Self-Supporting Tower (SST) and Roof Top (RT)). As such, four fuzzy
subtractive models were developed to represent the four classes. Sensitivity analysis
was carried to validate the model and observe the effect of clusters’ radius on models
performance.
Respati (2017) implemented forecasting optimization (STLF) using fuzzy
subtractive clustering method (FSC). Characteristics of the load anomaly patterns
showed inconsistency. Usually industrial activity stopped for a while and the workers
took time off from work a few days. Parameter setting for short term load forecasting
optimization (STLF) using fuzzy subtractive clustering method (FSC) which consisted
of three input parameters, cluster radius or influence range and epoch. The optimization
in this study was very influential in optimizing the value of forecasting accuracy that
has not been optimized.
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Another study conducted by Ramos, et al. (2017), using Noise Clustering,
Density Oriented Fuzzy C-Means algorithms, Kernel Fuzzy C-Means, and Dierential
Evolution algorithm. A design data driven based fault diagnosis systems using fuzzy
clustering techniques was presented. As a rest part of the classifcation process, the data
was pre-processed to eliminate outliers and reduce the confusion. To achieve this, the
Noise Clustering and Density Oriented Fuzzy C-Means algorithms were used.
Secondly, the Kernel Fuzzy C-Means algorithm was used to achieve greater separability
among the classes, and reduce the classifcation errors. Finally, a third step is developed
to optimize the two parameters used in the algorithms in the training stage using the
Dierential Evolution algorithm.
Mittal & Suman (2014) conducted the research using k-Means Clustering,
Hierarchical Clustering and Density. Data mining is covering every field of our life. In
this paper, provided an overview of the comparison, classification of clustering
algorithms. Under partitioning methods, applied k-means, and its variant k-medicine
weka tool. Under hierarchical, discussed the two approaches which are the top-down
approach and the bottom-up approach. The DBSCAN and OPTICS algorithms under
the density based methods. The STING and CLIQUE algorithms under the grid based
methods.
Next research was conducted by Tiwari & Yadav (2015) using Fuzzy
Subtractive Clustering and ANFIS. Applicability and capability of Fuzzy Subtractive
Clustering based approach to develop a prediction model prior to the implementation of
the actual machining has been investigated. Subtractive Clustering is a fast one-pass
algorithm for estimating the number of clusters and determining the cluster centres in a
set of data . In all three input variable were used, consisting of Spindle Speed S, Feed
rate F, and Depth of Cut DOC, and one output variable as tool vibration.
Pereira, et al. (2014) researched about Fuzzy Subtractive Clustering. This paper
focused on demand response in a smart grid scope using a fuzzy subtractive clustering
technique for modeling demand response. Domestic consumption was classified into
profiles in order to favorable cover the adequate modeling. The fuzzy subtractive
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clustering technique was applied to a case study of domestic consumption demand
response with three scenarios and a comparison of the results.
Radionov, Evdokimov, Sarlybaev, & Karandaeva (2015) conducted a study
using Subtractive Clustering. A promising diagnostic condition control technique for the
high-voltage oil-filled electrical facilities is the method of positioning partial discharges
(PDs) and their intense measuring. The paper provideds outcome of experiments
enabling acoustic PD positioning at the transformers of the power plant units. It
considered the methods and algorithm of processing results of the periodical acoustic
PD positioning based on the subtractive clustering technique.
Another study conducted by Rao, Sood, & Jarial (2015), using Subtractive
Clustering. This paper helped in tuning and designing the membership functions that are
best suited for the problem statement by integrating subtractive clustering method for
fuzzy expert system design. The proposed integrated design of clustering based fuzzy
expert system acted in improving the accuracy and leads to a précised decision making
environment.
Ahmad & Dang (2015) conducted a study using some method which are Simple K-
mean, DBSCAN, HCA and MDBCA. In this paper the four major clustering algorithms
namely Simple K-mean, DBSCAN, HCA and MDBCA were compared to identify the
performance of these four clustering algorithms. Performance of these four techniques
were presented and compared using a clustering tool WEKA. The results were tested on
different datasets namely Abalone, Bankdata, Router, SMS and Webtk dataset using
WEKA interface and compute instances, attributes and the time taken to build the
model.
Soni & Patel (2017) conducted a study using K-means and K-medoids Algorithm.
In this paper, they strived to compare K-means and Kmedoids algorithms using the
dataset of Iris plants from UCI Machine Learning Repository. The results obtained were
in favour of K medoids algorithm owing to its ability to be better at scalability for the
larger dataset and also due to it being more efficient than K-means. K-medoids showed
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its superiority over k means in execution time, sensitivity towards outlier data and to
reduce the noise.
Another study conducted by Rani & Rohil (2013) conducted research by
applying CURE, BIRCH, ROCK, CHEMELEON, Linkage, and Bisceting k-means. The
quality of a pure hierarchical clustering method suffered from its inability to perform
adjustment, once a merge or split decision has been executed. This paper presented an
overview of improved hierarchical clustering algorithm. Hierarchical clustering is a
method of cluster analysis which seeks to build a hierarchy of clusters.
Arumugadevi & Seenivasagam (2015) performed the research by implementing
Fuzzy C-Means (FCM) clustering and Self Organizing Map (SOM). Image
segmentation was the first step for any image processing based applications. The
Conventional methods are unable to produce good segmentation results for color
images. The researcher presented two soft computing approaches namely Fuzzy C-
Means (FCM) clustering and Self Organizing Map (SOM) network were used to
segment the color images. The segmentation results of FCM and SOM compared to the
results of K-Means clustering. The results shown that the Fuzzy C-Means and SOM
produced the better results than K-means for segmenting complex color images. The
time required for the training of SOM was higher.
Chitra & Maheswari (2017) performed the research using partition-based
algorithms, hierarchical based algorithms, and density-based algorithms. Clustering is a
significant task in data analysis and data mining applications. Clustering algorithms can
be classified into partition-based algorithms, hierarchical based algorithms, density-
based algorithms and grid-based algorithms. This paper focused on a keen study of
different clustering algorithms in data mining. In short, partitioning algorithms
attempted to determine k clusters that optimize a certain, often distance-based criterion
function.
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After making the inductive study, the research position for the researches can be seen in Table 2.1 below:
Table 2.1 Inductive Study
No Title Author
Fuzzy
C-
Means
Hierarc
hical
Cluster
ing
Optimi
zation
Fuzzy
Subtrac
tive
Noise
Cluster
ing
Dens
ity
Algori
thm
ANFIS K-
Medoids
Self
Organizing
Map
1
Possibilistic and fuzzy
clustering methods for
robust
Ferarro &
Giordani, 2017 √ - - - - - - - -
2
Fuzzy Clustering with
Nonlinearly
Transformed Data
Zhu, Pedrycz, &
Li, 2017 √ - √ - - - - - -
3
Predicting
Telecommunication
Tower Costs Using
Fuzzy Subtractive
Clustering
Marzouk &
Alaraby, 2012 - - - √ - - - - -
4
The Impact of
Influence Range Fuzzy
Subtractive Clustering
Modification to
Accuracy Anomalous
Load Forecasting
Respati, 2017 - - √ √ - - - - -
5
A novel fault diagnosis
scheme applying fuzzy
clustering
Ramos, et al.,
2017 √ - - - √ √ - - -
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32
No Title Author
Fuzzy
C-
Means
Hierarc
hical
Cluster
ing
Optimi
zation
Fuzzy
Subtrac
tive
Noise
Cluster
ing
Dens
ity
Algori
thm
ANFIS K-
Medoids
Self
Organizing
Map
6
Comparison and
Analysis of Various
Clustering Methods
Mittal &
Suman, 2014 √ √ - - - √ - - -
7
Fuzzy Subtractive
Clustering Based
Prediction Approach
for Machine Tool
Vibration
Tiwari &
Yadav, 2015 - - - √ - - √ - -
8
Fuzzy subtractive
clustering technique
applied to demand
response in a smart
grid scope
Pereira, et al,
2014 - - - √ - - - - -
9
Application of
subtractive clustering
for power transformer
fault diagnostics
Radionov, et al,
2015 - - - √ - - - - -
10
Subtractive clustering
Fuzzy Expert System
for Engineering
Applications
Rao, Sood, &
Jarial, 2015 - - - √ - - - - -
11
Performance
Evaluation of
Clustering Algorithm
Using Different
Dataset
Ahmad & Dang,
2015 √ - - - - - - - -
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33
No Title Author
Fuzzy
C-
Means
Hierarc
hical
Cluster
ing
Optimi
zation
Fuzzy
Subtrac
tive
Noise
Cluster
ing
Dens
ity
Algori
thm
ANFIS K-
Medoids
Self
Organizing
Map
12
Comparative Analysis
of K-means and K-
medoids
Soni & Patel,
2017 √ - - - - - - √ -
13
A Study of
Hierarchical Clustering
Algorithm
Rani & Rohil,
2013 √ √ - - - - - - -
14
Clustering Methods
with Qualitative Data:
A Mixed Methods
Approach for
Prevention Research
Arumugadevi &
Seenivasagam,
2015 √ - - - - - - - √
15
A Comparative Study
of Various Clustering
Algorithms in Data
Mining
Chitra &
Maheswari,
2017
- √ - - √ √ - - -
Comparison to the Author Research
Title Author
Fuzzy
C-
Means
Hierarc
hical
Cluster
ing
Optimi
zation
Fuzzy
Subtrac
tive
Noise
Cluster
ing
Dens
ity
Algori
thm
ANFIS K-
Medoids
Self
Organizing
Map
Comparison Study of Fuzzy C-
Means and Fuzzy Subtractive
Clustering Implementation for
Quality of IndiHome Fiber Optic
Network PT Telkom Indonesia
Astari,
2018 √ - - √ - - - - -
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34
CHAPTER III
RESEARCH METHODOLOGY
3.1 Research Flowchart
The research flowchart of this study is depicted in Figure 3.1 below:
Figure 2.1 Research Flowchart
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3.2 Problem Identification
Research is initiated by identifying the problems that exist within the concept of quality
maintenance, especially on quality of telecommunication network. Consumer
perceptions do not always result in the same judgment because not all consumers have
full knowledge of the condition of the product or service, which will have an impact on
IndiHome's buying interest. The company unaware on the quality of the system for each
customer. The company also unclassify the quality to be understood by its employees
which resulted in the lack of preparedness of the company to respond the complaints.
This research is conducted for grouping or clustering the quality system of IndiHome
fiber optic cable network using fuzzy clustering method in PT Telkom company and to
evaluate the performance obtained on Fuzzy Subtractive Clustering and Fuzzy C-Means
Clustering results.
3.3 Problem Formulation
From the problems found in the concept, furthermore, the formulation of the problem
according to the problem identification is identified. From the above conditions that
stated in problem identification the quality of IndiHome system PT Telkom Indonesia
branch of Yogyakarta determined by using clustering method with Fuzzy C-Means and
Fuzzy Subtractive Clustering based on predetermined criteria. Thus, the purpose of this
study is to form the cluster group members of the IndiHome fiber optic cable network
quality by implementing Fuzzy C-Means method and Fuzzy Subtractive Clustering.
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3.4 Literature Review
The literature review in accordance with the discussion are gathered. Literature review
consists of two types, deductive study and inductive study. Deductive studies are often
known by theoretical studies derived from the theories of experts who are often used as
a source of study. While the inductive study is a study derived from previous studies
that can be used as a reference or comparison between previous studies with the
research to avoid the existence of plagiarism.
3.5 Data Collection
Data collection methods are used to form the clustering group member of IndiHome
quality by using fuzzy subtractive clustering algorithm compare with fuzzy c-means
(FCM). The data were collected at PT. Telkom Indonesia (Yogyakarta) on March 2018.
The data that collected from the company is the primary data. The primary data will be
used for the main calculation and information for this research. The data were collected
by using some variables to get the performance result of fuzzy clustering method. The
type of data are:
a. Primary Data
Primary data in this study were obtained from direct observation by interviewing the
manager of the PT TELKOM in Yogyakarta. Interview was conducted with several
managers to identify the factors about the prediction of IndiHome network quality
according to the clustering method used in this particular task as well as some other
information on the operations. Then, historical data are is quantitative data obtained
from the manager of PT TELKOM Yogyakarta that contain the quality variable covering
some indicators or variables that affect the network performance such as Tx Power (the
path through which to send data between devices), Rx Power (commonly called
received which is useful to capture data transmitted by the transmitter or Tx Power),
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Temperature, Power Supply (component that supplies power at least one electric load),
and Bias Current (establishing predetermined voltages or currents at various point of an
electronic circuit for the purpose of establishing proper operating conditions in
electronic components) from both ONT (Optical Network Unit) from customer system
and OLT (Optical Network Termination) from company system.
b. Secondary Data
Secondary data obtained from literature-literature like journals, articles, explanation
from experts to find the information about methods and problems on this particular task.
3.6 Pre-Processing Data
In the KDD (Knowledge Discovery in Database) stage, preprocessing data is the second
stage in which a series of processes are used to clean up unnecessary data or if it is
wrong to fit the purpose and data will be ready for processing. In order for the research
process to run properly, the needs of data to be clustered need to be translated and
converted into data form in accordance with the clustering method used is the algorithm
with Fuzzy Subtractive Clustering modeling and Fuzzy C-Means modeling.
3.7 Data Processing
Preprocessing data are applied using tools or MATLAB and Microsoft Excel software
by applying both clustering techniques using Fuzzy Subtractive Clustering modeling
algorithm and using Fuzzy C-Means modeling.
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3.7.1 Fuzzy C-Means Processing
The parameters required in the clustering process are the number of clusters (c), the
rank (m), maximum iteration (MaxIter), the smallest expected error (x), the initial
objective function (P0), and the initial iteration (t). The outputs resulting from the
clustering process are the industries that fall into clusters (1 or 2 or 3 or 4) of different
kinds of quality: excellent, good, bad, and very bad then made into 4 clusters according
to the cluster number parameters. The first test is performed to get the minimum error
value (ξ). The error value is obtained by calculating the difference of the objective
function obtained on each iteration. The objective function will conclude as converged
if the resulting value is constant, so the error (error) produced is worth 0. In this test, the
cluster number parameter used is 4 with maximum 100 iterations.
3.7.2 Fuzzy Subtractive Clustering Processing
In the data processing, there are 4 parameters required for the formation of FIS model
that is 3 parameters follow the standard provisions of squash factor of 1.25, accept ratio
and reject ratio of 0.50 and 0.15 respectively and the radius value (r) used is a value
from range 0 to 1 (to obtain optimal cluster number). The accept ratio is the lower
bound in which a data point being a candidate cluster center is allowed to become a
cluster center. While the reject ratio is the upper limit in which a data point being a
candidate cluster center is not allowed to become a cluster center
3.8 Clustering Validation
After the clustering process is complete, the evaluation process proceeded by using PC
index and PE index to obtain the value of cluster validity. After the whole process is
complete, the output in the form of PC index and PE index values and quality groups
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will be acquired. The purpose of this test is to get the best value of c that has PC index
and the best PE index value addressed in subsequent tests. The test of cluster number is
done by comparing PC index and PE index values from different clusters for each
variation of radius which have been used in range 0.1 to 1 in Fuzzy Subtractive
Clustering, also in Fuzzy C-Means with the consideration of the number of clusters 4.
3.9 Discussion
After doing the data processing and obtaining the results with MATLAB software and
Microsoft Excel, then analysis of result discussion will be resumed. Then, the result will
be discussed by comparing the performance of Fuzzy Subtractive Clustering and Fuzzy
C-Means Clustering by considering the value of the PC index and PE index value. On
both artificial and real datasets, this algorithm is able, not only to determine the optimal
number of clusters but also to provide better clustering partitions than standard
algorithms.
3.10 Conclusion and Recommendation
The conclusion contains an explanation on the answer to the problem formulation that
was set at the beginning of the study briefly. In addition, there are suggestions or
recommendations that can be used by the hospitality and can also be used as further
research material.
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CHAPTER IV: DATA
COLLECTING AND PROCESSING
DATA COLLECTING AND PROCESSING
4.1 Data Collection
Data are collected from IndiHome status system information contained in each of the
existing ownership in the area of Yogyakarta in March 2018. The amount of data
processed that have experienced pre-processing are 100 data. The data are divided into
2 categories namely:
a. OLT (Optical Network Termination)
OLT is a device that becomes the endpoint, which is the root of an ODN. The
function of OLT is to control information going to both ways and to be on a server at
the head office. OLT is also called optical path termination, as a hardware endpoint
device on passive optical networks. OLT will send ethernet data to ONU.
b. ONU (Optical Network Unit)
Then, ONU (Optical Network Unit) or Optical Network Terminal (ONT) is a
customer-side device that provides both data, voice, and video interfaces. The ONU's
main function is to receive traffic in an optical format and convert it to the desired
shape, such as data, voice, and video.
The number of variables used is as many as 10 variables with both of categories include
data Tx Power, Rx Power, Temperature, Power Supply, and Bias Current as the factors
related in determining the quality of the network based on interviews conducted with
the manager of PT Telkom Yogyakarta. The data can be seen in Table 4.1. which are
used as a reference for model building.
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Table 4.1 Data Recapitulation IndiHome System
No
ONU - Optical Network Unit (from Customer) OLT - Optical Network Termination (from Company)
Tx Power
(dBm)
Rx
Power
(dBm)
Temperature
(ᵒC)
Power
Supply
(Volt)
Bias Current
(mA)
Tx Power
(dBm)
Rx
Power
(dBm)
Temperature
(ᵒC)
Power
Supply
(Volt)
Bias Current
(mA)
1 2.31 -24.09 50 3.34 17 3.7 -13.882 37 3.24 15
2 2.686 -15.392 38.941 3.28 12.85 2.85 -14.136 43 3.135 30.678
3 2.1 -19.28 42 3.24 13 3.67 -13.324 44 3.2 17
4 2.35 -17.03 40 3.26 11 3.86 -12.754 42 3.18 10
5 2.24 -17.3 50 3.24 11 3.67 -12.672 51 3.21 13
6 2.108 -20.088 55.383 3.22 16.1 0 -19.146 0 0 0
7 1.98 -31.54 42 3.28 12 4.05 -15.604 35 3.19 8
8 1.93 -33.97 43 3.26 10 3.76 -15.796 37 3.26 14
9 2.02 -15.49 40 3.28 12 3.49 -12.184 48 3.2 12
10 2.05 -21.25 48 3.28 12 3.41 -13.568 48 3.19 11
11 2.3 -18.15 47 3.28 14 3.79 -12.918 32 3.32 11
12 2.28 -18.66 42 3.24 10 3.61 -12.544 47 3.17 17
13 2.08 -16.73 50 3.3 8 3.65 -12.76 22 3.2 9
14 2.18 -17.05 45 3.28 7 3.81 -12.902 22 3.2 9
15 2.27 -19.58 43 3.32 13 3.67 -13.532 51 3.19 18
16 2.02 -18.89 56 3.28 10 3.9 -13.162 33 3.2 9
17 2.31 -20.81 47 3.26 12 3.84 -13.46 40 3.23 11
18 2 -16.32 52 3.28 9 4.01 -12.614 39 3.21 9
19 2.556 -20.758 51.406 3.18 21.148 3.514 -21.621 45 3.142 29.644
20 2.37 -24.68 45 3.3 13 4.1 -14.648 35 3.17 9
21 2.28 -16.55 45 3.18 8 3.57 -12.902 42 3.21 11
22 2.12 -17.98 41 3.24 8 4.08 -13.184 48 3.17 13
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No
ONU - Optical Network Unit (from Customer) OLT - Optical Network Termination (from Company)
Tx Power
(dBm)
Rx
Power
(dBm)
Temperature
(ᵒC)
Power
Supply
(Volt)
Bias Current
(mA)
Tx Power
(dBm)
Rx
Power
(dBm)
Temperature
(ᵒC)
Power
Supply
(Volt)
Bias Current
(mA)
23 2.25 -17.54 48 3.24 11 3.67 -12.836 36 3.24 13
24 2.1 -19.46 47 3.24 10 3.93 -13.122 35 3.18 10
25 2.42 -19.47 42.77 3.24 12.2 3.46 -21.627 39.1 3.212 12.214
26 2.35 -16.23 51 3.3 8 3.68 -12.77 45 3.21 17
27 1.99 -18.79 45 3.28 11 3.76 -13.074 40 3.23 11
28 2.14 -18.07 49 3.26 8 3.7 -12.938 29 3.24 15
29 2.03 -18.41 53 3.28 9 3.63 -12.934 37 3.3 13
30 2.16 -22.84 53 3.28 18 3.75 -14.186 36 3.23 11
31 2.582 -13.8 53.609 3.22 19.3 3.248 -15.08 59 3.148 41.481
32 2.31 -19.706 53.254 3.22 17.9 3.648 -20.893 41.105 3 30.014
33 2.23 -19.79 45 3.28 6 3.8 -13.286 40 3.2 11
34 2.24 -16.14 48 3.3 7 3.72 -12.708 49 3.19 11
35 2.24 -16.14 48 3.3 7 3.72 -12.708 49 3.19 11
36 2.18 -18.32 45 3.28 12 3.31 -12.648 35 3.18 11
37 2.32 -19.83 44 3.32 10 3.48 -13.216 42 3.2 7
38 1.86 -18.86 43 3.24 9 3.76 -13.424 27 3.17 14
39 2.35 -18.09 46 3.26 13 3.35 -12.632 45 3.18 11
40 2.02 -21.3 54 3.26 10 0 -13.938 0 0 0
41 2.28 -17.3 51 3.3 8 3.66 -12.654 33 3.33 14
42 2.03 -19.43 40 3.2 9 3.73 -12.614 46 3.21 18
43 2.15 -17.98 46 3.3 8 3.64 -13.046 39 3.18 9
44 2.204 98.064 44.535 3.2 12.6 3.53 -21.434 52 3.176 32.354
45 2.35 -19.39 50 3.3 16 4.05 -12.648 39 3.21 8
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No
ONU - Optical Network Unit (from Customer) OLT - Optical Network Termination (from Company)
Tx Power
(dBm)
Rx
Power
(dBm)
Temperature
(ᵒC)
Power
Supply
(Volt)
Bias Current
(mA)
Tx Power
(dBm)
Rx
Power
(dBm)
Temperature
(ᵒC)
Power
Supply
(Volt)
Bias Current
(mA)
46 2.22 -19.17 52 3.28 9 3.75 -13.348 31 3.2 10
47 2.04 -21.94 50 3.3 7 3.75 -13.888 39 3.28 15
48 2.19 -18.09 63 3.28 10 3.64 -12.78 37 3.21 7
49 2.27 -26.57 44 3.32 11 3.66 -13.99 48 3.17 11
50 2.59 -24.09 52.902 3.18 14 3.789 -23.027 52.167 3 29.468
51 2.27 -20.75 53 3.28 9 3.42 -13.718 55 3.21 16
52 1.94 -18.01 47 3.26 12 3.75 -12.836 37 3.34 12
53 2.17 -18.29 52 3.28 8 3.9 -13.174 52 3.2 13
54 2.02 -14.95 53 3.28 10 3.73 -12.43 45 3.23 16
55 2.29 -18.18 50 3.22 10 4.03 -12.644 38 3.21 9
56 2.26 -19.7 43 3.28 11 3.95 -13.24 50 3.22 9
57 2.16 -17.85 54 3.3 7 3.69 -12.888 35 3.3 11
58 2.612 -23.098 46.656 3.2 16.1 0 -17.122 0 0 0
59 2.16 -21.25 36 3.28 7 3.96 -13.638 37 3.21 7
60 2.38 -13.65 47 3.32 14 4.11 -12.398 43 3.19 8
61 2.134 -18.014 48.102 3.2 9.7 0 -17.748 0 0 0
62 2.21 -20.97 46 3.3 14 3.69 -13.336 40 3.16 10
63 3.23 -23.98 54.574 3.26 16.866 0 -17.214 0 0 0
64 2.476 13.316 58.602 3.3 13.65 0 -23.962 0 0 0
65 2.31 -15.34 47 3.3 14 3.68 -12.43 47 3.21 12
66 2.25 -19.13 46 3.32 14 3.66 -13.274 40 3.16 10
67 2.394 -18.24 44.039 3.2 13.7 0 -14.922 0 0 0
68 2.34 -23.37 46 3.28 13 3.7 -13.912 38 3.2 8
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No
ONU - Optical Network Unit (from Customer) OLT - Optical Network Termination (from Company)
Tx Power
(dBm)
Rx
Power
(dBm)
Temperature
(ᵒC)
Power
Supply
(Volt)
Bias Current
(mA)
Tx Power
(dBm)
Rx
Power
(dBm)
Temperature
(ᵒC)
Power
Supply
(Volt)
Bias Current
(mA)
69 2.588 22.22 41.707 3.2 12.55 0 -16.99 0 0 0
70 2.89 -19.47 53.254 3.2 19.4 0 -14.934 0 0 0
71 2.14 -19.39 48 3.24 12 3.69 -13.054 48 3.21 12
72 2.05 -28.862 45.242 3.2 13.9 0 -17.8 0 0 0
73 2.504 -22.758 50.418 3.2 16.05 0 -20.704 0 0 0
74 2.07 -22.44 44 3.28 13 3.56 -13.99 42 3.2 7
75 2.364 -24.814 46.781 3.28 9.4 0 -22.68 0 0 0
76 2.338 -18.762 51.129 3.2 16.85 0 -26.022 0 0 0
77 2.33 -15.78 49 3.3 15 3.6 -12.714 36 3.2 8
78 3.184 -24.684 63.016 3.28 16.908 0 -17.056 0 0 0
79 2.178 98.064 44.535 3.2 12.45 3.473 -21.407 52 3.173 32.236
80 2.16 -16.34 47 3.24 11 3.67 12.814 46 3.21 9
81 2.13 -18.5 42 3.26 8 3.69 -12.992 37 3.19 11
82 2.27 -20.5 48 3.24 14 3.75 -13.228 38 3.32 12
83 3.42 -19.788 51.012 3.32 11.396 0 -23.768 0 0 0
84 2.538 -15.592 47.938 3.22 16.55 0 -23.012 0 0 0
85 2.15 -18.44 47 3.28 9 3.73 -13.46 36 3.28 14
86 1.94 -18.82 54 3.26 5 3.42 -13.44 56 3.21 17
87 2.02 -18.63 55 3.18 10 3.61 -12.976 48 3.16 12
88 2.32 -27.96 48 3.28 11 3.8 -15.31 28 3.2 6
89 2.172 -22.678 52.191 3.22 16.9 0 -18.894 0 0 0
90 3.202 -18.664 52.992 3.28 13.962 0 -24.89 0 0 0
91 2.28 -19.39 53 3.3 9 3.73 -13.52 38 3.26 14
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No
ONU - Optical Network Unit (from Customer) OLT - Optical Network Termination (from Company)
Tx Power
(dBm)
Rx
Power
(dBm)
Temperature
(ᵒC)
Power
Supply
(Volt)
Bias Current
(mA)
Tx Power
(dBm)
Rx
Power
(dBm)
Temperature
(ᵒC)
Power
Supply
(Volt)
Bias Current
(mA)
92 2.02 -17.37 52 3.24 7 3.87 -12.754 40 3.2 9
93 2.502 -16.576 47.363 3.22 16.65 0 -21.55 0 0 0
94 2.33 -23.46 45 3.2 9 3.82 -13.734 39 3.23 11
95 2.21 -24.95 45 3.3 13 3.97 -14.842 35 3.17 9
96 2.344 -18.182 44.891 3.22 13.85 0 -21.74 0 0 0
97 2.468 -20.058 55.602 3.3 10.214 0 -19.21 0 0 0
98 2.17 -18.99 50 3.24 13 3.83 -12.684 35 3.22 9
99 2.74 -20.606 49 3.18 15.85 0 -20.52 0 0 0
100 2.23 -18.69 52 3.28 10 3.64 -12.918 36 3.28 14
4.2 Pre-Processing Data
Preprocessing is the stage where the selection of data are processed and changed to be more structured. In this case, the preprocessing stages
of data include:
a. Data Cleaning
Data cleaning is eliminating false data values, fixing data clutter and checking inconsistent data. The data that has been labeled as
incomplete or lack of attribute values. Therefore, incomplete data is not used or discarded and replaced with new data.
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b. Data Integration
Data integration are merged data from multiple sources. Combination of technical
and business processes used to combine data from disparate sources into meaningful
and valuable information.
4.3 Data Processing
At this stage, we will present the steps of applying clustering techniques to both Fuzzy
C-Means and Fuzzy Subtractive Clustering methods using Matlab and Microsoft Excel
software.
4.3.1 Fuzzy C-Means Processing
Clustering process is done using the input data, which are:
n = 100 (there are 100 historical data quality system performances)
m = 10 (there are ten criteria that are Tx Power, Rx Power, Temperature,
Power Supply, and Bias Current in ONU and Tx Power, Rx Power,
Temperature, Power Supply, and Bias Current in OLT)
According to Prihatini, P. M. (2015), the values used for parameter initialization are:
C = 4 (4 clusters)
m = 2 (ranks for the partition matrix)
MaxIter = 100
ξ = 0,000016 (least expected error)
P0 = 0 (initial objective function is 0)
t = 1 (initial iteration is 1)
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By using MATLAB R2013a Software, the calculation result is center cluster or
center, the degree of membership or matrix U and value of an objective function or
ObjFcn. The first result is the result of functional value calculation, as follows:
X = load(‘data.dat’);
[Center, U, ObjFcn]=fcm(X,4);
Iteration count = 1, obj. fcn = 24348.721886
Iteration count = 2, obj. fcn = 18293.255652
Iteration count = 3, obj. fcn = 17336.118489
Iteration count = 4, obj. fcn = 15924.139002
Iteration count = 5, obj. fcn = 14008.353018
Iteration count = 6, obj. fcn = 13275.303860
Iteration count = 7, obj. fcn = 13094.172823
Iteration count = 8, obj. fcn = 12922.304448
Iteration count = 9, obj. fcn = 12445.800347
Iteration count = 10, obj. fcn = 10861.606226
Iteration count = 11, obj. fcn = 7876.017889
Iteration count = 12, obj. fcn = 7263.455978
Iteration count = 13, obj. fcn = 7262.034144
Iteration count = 14, obj. fcn = 7261.993259
Iteration count = 15, obj. fcn = 7261.981248
Iteration count = 16, obj. fcn = 7261.977304
Iteration count = 17, obj. fcn = 7261.975987
Iteration count = 18, obj. fcn = 7261.975544
Iteration count = 19, obj. fcn = 7261.975395
Iteration count = 20, obj. fcn = 7261.975345
Iteration count = 21, obj. fcn = 7261.975328
Iteration count = 22, obj. fcn = 7261.975322
Interpretation, software MATLAB R2013a. It requires 22 iterations before
obtaining the optimal solution for the functional value of 7261.975322. The iteration
process stops at the 22nd iteration where the value | 𝑃𝑡 - 𝑃𝑡 - 1 | <ξ. To further illustrate
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it can be seen in Figure 4.1 graph relationship between objective function with the
number of iterations in the figure below:
Figure 4.1 Relationship between Objective Function with the Number of Iterations
From the picture above can be seen that the value of the minimum objective
function achieved by the iteration process as much as 22 times or function is converged
with the iteration process as much as 22 times. The second result is the result of the
calculation of vij values as follows:
Center =
1.0e+04 *
2.217 -18.603 47.078 3.264 10.857 3.646 -13.323 46.073 3.176 14.077
2.193 97.369 44.561 3.200 12.533 3.481 -21.388 51.699 3.156 32.102
2.554 -19.688 50.592 3.233 14.455 0.038 -19.695 0.335 0.033 0.139
2.196 -19.559 48.047 3.271 11.048 3.729 -13.387 36.675 3.207 11.343
At the last iteration (the 22nd iteration), the vkj cluster center produced by the software
Matlab with k = 1,2,3,4; and j = 1,2,3,4,5,6,7,8,9,10 are:
2.217 -18.603 47.078 3.264 10.857 3.646 -13.323 46.073 3.176 14.077
2.193 97.369 44.561 3.200 12.533 3.481 -21.388 51.699 3.156 32.102
2.554 -19.688 50.592 3.233 14.455 0.038 -19.695 0.335 0.033 0.139
2.196 -19.559 48.047 3.271 11.048 3.729 -13.387 36.675 3.207 11.343
0
5000
10000
15000
20000
25000
30000
1 3 5 7 9 11 13 15 17 19 21
Ob
j. F
un
cti
on
Iteration
Relationship
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The second result is the degree of membership values. Fuzzy c-means has a
membership degree that is useful for grouping data into appropriate clusters. The result
shows as follows in Table 4.2:
Table 4.2 Degree of Membership
Data µi1 µi2 µi3 µi4 Data µi1 µi2 µi3 µi4
1 0.3046 0.0032 0.0295 0.6627 38 0.2313 0.0061 0.0842 0.6784
2 0.5377 0.0153 0.0667 0.3803 39 0.8173 0.001 0.0064 0.1753
3 0.7308 0.0023 0.0137 0.2532 40 0.0262 0.0035 0.9294 0.0409
4 0.5275 0.0033 0.0223 0.4469 41 0.1786 0.0025 0.0254 0.7935
5 0.8463 0.0022 0.0108 0.1406 42 0.724 0.0036 0.0194 0.2529
6 0.0104 0.0015 0.9722 0.016 43 0.2366 0.0014 0.0119 0.7501
7 0.3276 0.0067 0.0771 0.5886 44 0 0.9999 0 0
8 0.3866 0.0074 0.0712 0.5348 45 0.2642 0.0022 0.0199 0.7137
9 0.7331 0.0039 0.0197 0.2433 46 0.1589 0.003 0.0381 0.8001
10 0.847 0.0013 0.0077 0.144 47 0.3376 0.002 0.0158 0.6447
11 0.1316 0.002 0.0238 0.8426 48 0.3526 0.0094 0.0833 0.5547
12 0.8183 0.0022 0.0114 0.1682 49 0.6733 0.0037 0.0229 0.3001
13 0.2193 0.0094 0.2049 0.5664 50 0.5645 0.0168 0.0692 0.3494
14 0.2272 0.0098 0.2 0.563 51 0.728 0.0064 0.0277 0.2379
15 0.8019 0.0036 0.0165 0.178 52 0.0565 0.0004 0.0032 0.94
16 0.2201 0.0042 0.0483 0.7274 53 0.7758 0.0038 0.0181 0.2022
17 0.2176 0.0008 0.0064 0.7752 54 0.703 0.0029 0.0163 0.2778
18 0.2716 0.0022 0.0175 0.7087 55 0.126 0.0009 0.008 0.8651
19 0.517 0.0162 0.0777 0.3891 56 0.7635 0.0032 0.0168 0.2165
20 0.195 0.0024 0.0275 0.775 57 0.221 0.003 0.0296 0.7464
21 0.5598 0.0018 0.012 0.4265 58 0.0146 0.0019 0.9608 0.0227
22 0.7779 0.0029 0.0149 0.2043 59 0.3717 0.0068 0.0598 0.5617
23 0.0672 0.0005 0.0046 0.9277 60 0.5289 0.0033 0.0215 0.4463
24 0.0467 0.0005 0.0047 0.9481 61 0.0145 0.002 0.9609 0.0226
25 0.4062 0.0041 0.0332 0.5565 62 0.2799 0.0013 0.0112 0.7076
26 0.7582 0.0022 0.0124 0.2272 63 0.018 0.0024 0.9519 0.0277
27 0.2914 0.001 0.0082 0.6993 64 0.1754 0.0577 0.5411 0.2258
28 0.2052 0.0044 0.054 0.7364 65 0.8274 0.0017 0.009 0.1619
29 0.2095 0.0018 0.0158 0.7728 66 0.2826 0.0013 0.0104 0.7056
30 0.27 0.0038 0.0395 0.6867 67 0.0269 0.0037 0.9277 0.0417
31 0.5073 0.0424 0.1021 0.3482 68 0.2103 0.0018 0.0175 0.7704
32 0.4887 0.0149 0.08 0.4164 69 0.2059 0.0888 0.4522 0.2531
33 0.3716 0.002 0.0151 0.6113 70 0.0209 0.0029 0.944 0.0322
34 0.8058 0.0024 0.0123 0.1795 71 0.9182 0.0007 0.004 0.077
35 0.8058 0.0024 0.0123 0.1795 72 0.0419 0.0053 0.8886 0.0642
36 0.099 0.001 0.0096 0.8905 73 0.0053 0.0007 0.9859 0.0081
37 0.4433 0.0024 0.0182 0.5361 74 0.4315 0.0027 0.0219 0.5439
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Data µi1 µi2 µi3 µi4 Data µi1 µi2 µi3 µi4
75 0.0282 0.0037 0.9249 0.0432 88 0.2343 0.0067 0.122 0.6371
76 0.0176 0.0026 0.9535 0.0264 89 0.0073 0.001 0.9803 0.0113
77 0.1986 0.0024 0.0234 0.7756 90 0.0132 0.0019 0.9648 0.02
78 0.0603 0.0085 0.8409 0.0902 91 0.2601 0.0019 0.0159 0.7221
79 0 0.9999 0 0 92 0.3341 0.0025 0.0194 0.644
80 0.4609 0.0224 0.1003 0.4164 93 0.0113 0.0017 0.9698 0.0172
81 0.2672 0.0024 0.0204 0.71 94 0.2697 0.0016 0.0141 0.7146
82 0.1227 0.0007 0.0063 0.8703 95 0.2017 0.0026 0.029 0.7667
83 0.0106 0.0015 0.9716 0.0162 96 0.0156 0.0022 0.9583 0.0239
84 0.0152 0.0023 0.9594 0.0231 97 0.017 0.0024 0.9545 0.0262
85 0.1172 0.0009 0.0078 0.8741 98 0.0925 0.001 0.0111 0.8954
86 0.6834 0.0093 0.0365 0.2708 99 0.0025 0.0003 0.9932 0.0039
87 0.6976 0.0036 0.0198 0.279 100 0.1637 0.0015 0.0133 0.8216
The output of Fuzzy C-Means is a central cluster and some degree of membership
for each data point. This will provide information on the similarity of each object. One
of fuzzy clustering algorithms used is the fuzzy clustering c means algorithm. The
vector of fuzzy clustering, V = {v1, v2, v3, ..., vc}, is an objective function that is
defined by the degree of membership of the data Xj and the center of cluster Vj. Fuzzy
clustering is the process of determining the degree of membership. This information can
be used to build a fuzzy inference system. The degree of membership refers to how
likely a data can be a member of a cluster. The position and value of the matrix are
constructed randomly. Where the value of the membership lies on the interval 0 to 1. An
IndiHome system has a certain degree of membership to become a member of a cluster.
Certainly, the greatest degree of membership shows the highest tendency of a cluster
system to enter a cluster member. The degree of membership of each system in each
cluster is shown in the following Table 4.3.
Table 4.3 Clustering Result
Data Degree of membership on cluster Data tends to get into the cluster
1 2 3 4 1 2 3 4
1 0.3046 0.0032 0.0295 0.6627
*
2 0.5377 0.0153 0.0667 0.3803 x
3 0.7308 0.0023 0.0137 0.2532 x
4 0.5275 0.0033 0.0223 0.4469 x
5 0.8463 0.0022 0.0108 0.1406 x
6 0.0104 0.0015 0.9722 0.016
+
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51
Data Degree of membership on cluster Data tends to get into the cluster
1 2 3 4 1 2 3 4
7 0.3276 0.0067 0.0771 0.5886
*
8 0.3866 0.0074 0.0712 0.5348
*
9 0.7331 0.0039 0.0197 0.2433 x
10 0.847 0.0013 0.0077 0.144 x
11 0.1316 0.002 0.0238 0.8426
*
12 0.8183 0.0022 0.0114 0.1682 x
13 0.2193 0.0094 0.2049 0.5664
*
14 0.2272 0.0098 0.2 0.563
*
15 0.8019 0.0036 0.0165 0.178 x
16 0.2201 0.0042 0.0483 0.7274
*
17 0.2176 0.0008 0.0064 0.7752
*
18 0.2716 0.0022 0.0175 0.7087
*
19 0.517 0.0162 0.0777 0.3891 x
20 0.195 0.0024 0.0275 0.775
*
21 0.5598 0.0018 0.012 0.4265 x
22 0.7779 0.0029 0.0149 0.2043 x
23 0.0672 0.0005 0.0046 0.9277
*
24 0.0467 0.0005 0.0047 0.9481
*
25 0.4062 0.0041 0.0332 0.5565
*
26 0.7582 0.0022 0.0124 0.2272 x
27 0.2914 0.001 0.0082 0.6993
*
28 0.2052 0.0044 0.054 0.7364
*
29 0.2095 0.0018 0.0158 0.7728
*
30 0.27 0.0038 0.0395 0.6867
*
31 0.5073 0.0424 0.1021 0.3482 x
32 0.4887 0.0149 0.08 0.4164 x
33 0.3716 0.002 0.0151 0.6113
*
34 0.8058 0.0024 0.0123 0.1795 x
35 0.8058 0.0024 0.0123 0.1795 x
36 0.099 0.001 0.0096 0.8905
*
37 0.4433 0.0024 0.0182 0.5361
*
38 0.2313 0.0061 0.0842 0.6784
*
39 0.8173 0.001 0.0064 0.1753 x
40 0.0262 0.0035 0.9294 0.0409
+
41 0.1786 0.0025 0.0254 0.7935
*
42 0.724 0.0036 0.0194 0.2529 x
43 0.2366 0.0014 0.0119 0.7501
*
44 0 0.9999 0 0
o
45 0.2642 0.0022 0.0199 0.7137
*
46 0.1589 0.003 0.0381 0.8001
*
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52
Data Degree of membership on cluster Data tends to get into the cluster
1 2 3 4 1 2 3 4
47 0.3376 0.002 0.0158 0.6447
*
48 0.3526 0.0094 0.0833 0.5547
*
49 0.6733 0.0037 0.0229 0.3001 x
50 0.5645 0.0168 0.0692 0.3494 x
51 0.728 0.0064 0.0277 0.2379 x
52 0.0565 0.0004 0.0032 0.94
*
53 0.7758 0.0038 0.0181 0.2022 x
54 0.703 0.0029 0.0163 0.2778 x
55 0.126 0.0009 0.008 0.8651
*
56 0.7635 0.0032 0.0168 0.2165 x
57 0.221 0.003 0.0296 0.7464
*
58 0.0146 0.0019 0.9608 0.0227
+
59 0.3717 0.0068 0.0598 0.5617
*
60 0.5289 0.0033 0.0215 0.4463 x
61 0.0145 0.002 0.9609 0.0226
+
62 0.2799 0.0013 0.0112 0.7076
*
63 0.018 0.0024 0.9519 0.0277
+
64 0.1754 0.0577 0.5411 0.2258
+
65 0.8274 0.0017 0.009 0.1619 x
66 0.2826 0.0013 0.0104 0.7056
*
67 0.0269 0.0037 0.9277 0.0417
+
68 0.2103 0.0018 0.0175 0.7704
*
69 0.2059 0.0888 0.4522 0.2531
+
70 0.0209 0.0029 0.944 0.0322
*
71 0.9182 0.0007 0.004 0.077 x
72 0.0419 0.0053 0.8886 0.0642
+
73 0.0053 0.0007 0.9859 0.0081
+
74 0.4315 0.0027 0.0219 0.5439
*
75 0.0282 0.0037 0.9249 0.0432
+
76 0.0176 0.0026 0.9535 0.0264
+
77 0.1986 0.0024 0.0234 0.7756
*
78 0.0603 0.0085 0.8409 0.0902
+
79 0 0.9999 0 0
o
80 0.4609 0.0224 0.1003 0.4164 x
81 0.2672 0.0024 0.0204 0.71
*
82 0.1227 0.0007 0.0063 0.8703
*
83 0.0106 0.0015 0.9716 0.0162
+
84 0.0152 0.0023 0.9594 0.0231
+
85 0.1172 0.0009 0.0078 0.8741
*
86 0.6834 0.0093 0.0365 0.2708 x
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53
Data Degree of membership on cluster Data tends to get into the cluster
1 2 3 4 1 2 3 4
87 0.6976 0.0036 0.0198 0.279 x
88 0.2343 0.0067 0.122 0.6371
*
89 0.0073 0.001 0.9803 0.0113
+
90 0.0132 0.0019 0.9648 0.02
*
91 0.2601 0.0019 0.0159 0.7221
*
92 0.3341 0.0025 0.0194 0.644
*
93 0.0113 0.0017 0.9698 0.0172
+
94 0.2697 0.0016 0.0141 0.7146
*
95 0.2017 0.0026 0.029 0.7667
*
96 0.0156 0.0022 0.9583 0.0239
+
97 0.017 0.0024 0.9545 0.0262
+
98 0.0925 0.001 0.0111 0.8954
*
99 0.0025 0.0003 0.9932 0.0039
+
100 0.1637 0.0015 0.0133 0.8216
*
From the degree of membership in the last iteration can be obtained information
on the tendency for each observation goes into which cluster. The greatest degree of
membership shows that the highest tendency of observation to enter into a particular
cluster member. At the first observation, the membership degree value for the first
cluster is 0.3046 while the membership degree value for the second cluster is 0.0032.
Then, the membership degree value for the third cluster is 0.0295. After that, the
membership degree value for the fourth cluster is 0.6627. From that value, the first
observation entered in the fourth cluster. That's because the first observation has the
highest degree of membership in the fourth cluster rather than the other cluster.
Furthermore, on the second observation the value of membership degrees for the
first cluster is 0.5377. While the degree of membership for the second cluster is 0.0153.
Then, the membership degree value for the third cluster is 0.0667. After that, the
membership degree value for the fourth cluster is 0.3803. From that value, the second
observation entered in the first cluster.
The determination continues until the 100th observation, with a membership
degree value for the first cluster of 0.1637 while the membership degree value for the
second cluster is 0.0015. Then, the membership degree value for the third cluster is
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54
0.0133. After that, the membership degree value for the fourth cluster is 0.8216. From
that value, the 100th observation entered in the fourth cluster. Figure 4.2 shows the plot
of data for each cluster in 4 clusters.
Figure 4.2 Data Plot for Each Cluster in 4 Clusters
Information:
x = cluster 1
o = cluster 2
+ = cluster 3
* = cluster 4
The end result of the clustering of 100 IndiHome system quality data with ten
criteria are generate into 4 clusters as follows:
a. Group 1 (cluster 1), contains some of the data with the number 6, 40, 58, 61, 63, 64,
67, 69, 70, 72, 73, 75, 76, 78, 83, 84, 89, 90, 93, 96, 97, and 99
b. Group 2 (cluster 2), contains some of the data with the number 2, 3, 5, 9, 10, 12, 15,
19, 22, 26, 31, 32, 34, 35, 39, 42, 44, 49, 50, 51, 53, 54, 56, 65, 71, 79, 80, 86, and 87
c. Group 3 (cluster 3), contains some of the data with the number 1, 11, 13, 14, 16, 18,
23, 24, 28, 29, 30, 36, 38, 41, 46, 47, 48, 55, 57, 77, 85, 88, 91, 92, 98, and 100
1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6-40
-20
0
20
40
60
80
100
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55
d. Group 4 (cluster 4), contains some of the data with the number 4, 7, 8, 17, 20, 21, 25,
27, 33, 37, 43, 45, 52, 59, 60, 62, 66, 68, 74, 81, 82, 94, and 95
4.3.2 Fuzzy C-Means Validation
Next, the clustering validity on Fuzzy C-Means method is carried out with 2 indicators
as follows.
a. Partition Coefficient Index (PCI)
To calculate the value of PCI, the Equation 2.13 is employed. The result of PCI
validation on Fuzzy C-Means method is shown in Table 4.4.
Table 4.4 PCI Result on Fuzzy C-Means
Data µi12 µi2
2 µi3
2 µi4
2 Data µi1
2 µi2
2 µi3
2 µi4
2
1 0.0928 0.0000 0.0009 0.4392 22 0.6051 0.0000 0.0002 0.0417
2 0.2891 0.0002 0.0044 0.1446 23 0.0045 0.0000 0.0000 0.8606
3 0.5341 0.0000 0.0002 0.0641 24 0.0022 0.0000 0.0000 0.8989
4 0.2783 0.0000 0.0005 0.1997 25 0.1650 0.0000 0.0011 0.3097
5 0.7162 0.0000 0.0001 0.0198 26 0.5749 0.0000 0.0002 0.0516
6 0.0001 0.0000 0.9452 0.0003 27 0.0849 0.0000 0.0001 0.4890
7 0.1073 0.0000 0.0059 0.3464 28 0.0421 0.0000 0.0029 0.5423
8 0.1495 0.0001 0.0051 0.2860 29 0.0439 0.0000 0.0002 0.5972
9 0.5374 0.0000 0.0004 0.0592 30 0.0729 0.0000 0.0016 0.4716
10 0.7174 0.0000 0.0001 0.0207 31 0.2574 0.0018 0.0104 0.1212
11 0.0173 0.0000 0.0006 0.7100 32 0.2388 0.0002 0.0064 0.1734
12 0.6696 0.0000 0.0001 0.0283 33 0.1381 0.0000 0.0002 0.3737
13 0.0481 0.0001 0.0420 0.3208 34 0.6493 0.0000 0.0002 0.0322
14 0.0516 0.0001 0.0400 0.3170 35 0.6493 0.0000 0.0002 0.0322
15 0.6430 0.0000 0.0003 0.0317 36 0.0098 0.0000 0.0001 0.7930
16 0.0484 0.0000 0.0023 0.5291 37 0.1965 0.0000 0.0003 0.2874
17 0.0473 0.0000 0.0000 0.6009 38 0.0535 0.0000 0.0071 0.4602
18 0.0738 0.0000 0.0003 0.5023 39 0.6680 0.0000 0.0000 0.0307
19 0.2673 0.0003 0.0060 0.1514 40 0.0007 0.0000 0.8638 0.0017
20 0.0380 0.0000 0.0008 0.6006 41 0.0319 0.0000 0.0006 0.6296
21 0.3134 0.0000 0.0001 0.1819 42 0.5242 0.0000 0.0004 0.0640
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56
Data µi12 µi2
2 µi3
2 µi4
2 Data µi1
2 µi2
2 µi3
2 µi4
2
43 0.0560 0.0000 0.0001 0.5627 72 0.0018 0.0000 0.7896 0.0041
44 0.0000 0.9998 0.0000 0.0000 73 0.0000 0.0000 0.9720 0.0001
45 0.0698 0.0000 0.0004 0.5094 74 0.1862 0.0000 0.0005 0.2958
46 0.0252 0.0000 0.0015 0.6402 75 0.0008 0.0000 0.8554 0.0019
47 0.1140 0.0000 0.0002 0.4156 76 0.0003 0.0000 0.9092 0.0007
48 0.1243 0.0001 0.0069 0.3077 77 0.0394 0.0000 0.0005 0.6016
49 0.4533 0.0000 0.0005 0.0901 78 0.0036 0.0001 0.7071 0.0081
50 0.3187 0.0003 0.0048 0.1221 79 0.0000 0.9998 0.0000 0.0000
51 0.5300 0.0000 0.0008 0.0566 80 0.2124 0.0005 0.0101 0.1734
52 0.0032 0.0000 0.0000 0.8836 81 0.0714 0.0000 0.0004 0.5041
53 0.6019 0.0000 0.0003 0.0409 82 0.0151 0.0000 0.0000 0.7574
54 0.4942 0.0000 0.0003 0.0772 83 0.0001 0.0000 0.9440 0.0003
55 0.0159 0.0000 0.0001 0.7484 84 0.0002 0.0000 0.9204 0.0005
56 0.5829 0.0000 0.0003 0.0469 85 0.0137 0.0000 0.0001 0.7641
57 0.0488 0.0000 0.0009 0.5571 86 0.4670 0.0001 0.0013 0.0733
58 0.0002 0.0000 0.9231 0.0005 87 0.4866 0.0000 0.0004 0.0778
59 0.1382 0.0000 0.0036 0.3155 88 0.0549 0.0000 0.0149 0.4059
60 0.2797 0.0000 0.0005 0.1992 89 0.0001 0.0000 0.9610 0.0001
61 0.0002 0.0000 0.9233 0.0005 90 0.0002 0.0000 0.9308 0.0004
62 0.0783 0.0000 0.0001 0.5007 91 0.0677 0.0000 0.0003 0.5214
63 0.0003 0.0000 0.9061 0.0008 92 0.1116 0.0000 0.0004 0.4147
64 0.0308 0.0033 0.2928 0.0510 93 0.0001 0.0000 0.9405 0.0003
65 0.6846 0.0000 0.0001 0.0262 94 0.0727 0.0000 0.0002 0.5107
66 0.0799 0.0000 0.0001 0.4979 95 0.0407 0.0000 0.0008 0.5878
67 0.0007 0.0000 0.8606 0.0017 96 0.0002 0.0000 0.9183 0.0006
68 0.0442 0.0000 0.0003 0.5935 97 0.0003 0.0000 0.9111 0.0007
69 0.0424 0.0079 0.2045 0.0641 98 0.0086 0.0000 0.0001 0.8017
70 0.0004 0.0000 0.8911 0.0010 99 0.0000 0.0000 0.9864 0.0000
71 0.8431 0.0000 0.0000 0.0059 100 0.0268 0.0000 0.0002 0.6750
Here is the calculation of the PCI value:
PCI =
= 0.662786731
The value of the PCI (Partition Coefficient Index) is 0.662786731.
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57
b. Partition Entropy Index (PEI)
To calculate the value of PEI, the Equation 2.14 is employed. The result of PEI
validation on Fuzzy C-Means method is shown in Table 4.5.
Table 4.5 PEI Result on Fuzzy C-Means
Data µi1 µi2 µi3 µi4 Data µi1 µi2 µi3 µi4
1 -0.169 -0.058 -0.104 -0.273 35 -0.119 -0.035 -0.054 -0.308
2 -0.268 -0.123 -0.181 -0.368 36 -0.119 -0.035 -0.045 -0.103
3 -0.102 -0.028 -0.059 -0.348 37 -0.101 -0.028 -0.073 -0.334
4 -0.119 -0.035 -0.085 -0.360 38 -0.318 -0.174 -0.208 -0.263
5 -0.129 -0.039 -0.049 -0.276 39 -0.057 -0.013 -0.032 -0.305
6 -0.024 -0.091 -0.027 -0.066 40 -0.046 -0.144 -0.068 -0.131
7 -0.290 -0.144 -0.198 -0.312 41 -0.182 -0.065 -0.093 -0.184
8 -0.275 -0.130 -0.188 -0.335 42 -0.142 -0.045 -0.076 -0.348
9 -0.143 -0.046 -0.077 -0.344 43 -0.076 -0.019 -0.053 -0.216
10 -0.097 -0.027 -0.037 -0.279 44 -0.357 -0.333 0.000 0.000
11 -0.204 -0.078 -0.089 -0.144 45 -0.126 -0.038 -0.078 -0.241
12 -0.117 -0.034 -0.051 -0.300 46 -0.251 -0.110 -0.124 -0.178
13 -0.365 -0.314 -0.325 -0.322 47 -0.095 -0.026 -0.066 -0.283
14 -0.366 -0.307 -0.322 -0.323 48 -0.296 -0.150 -0.207 -0.327
15 -0.155 -0.051 -0.068 -0.307 49 -0.156 -0.052 -0.086 -0.361
16 -0.253 -0.111 -0.146 -0.232 50 -0.279 -0.133 -0.185 -0.367
17 -0.036 -0.007 -0.032 -0.197 51 -0.193 -0.071 -0.099 -0.342
18 -0.105 -0.030 -0.071 -0.244 52 -0.056 -0.013 -0.018 -0.058
19 -0.287 -0.141 -0.199 -0.367 53 -0.155 -0.051 -0.073 -0.323
20 -0.194 -0.072 -0.099 -0.198 54 -0.109 -0.031 -0.067 -0.356
21 -0.055 -0.013 -0.053 -0.363 55 -0.082 -0.021 -0.039 -0.125
22 -0.130 -0.040 -0.063 -0.324 56 -0.141 -0.045 -0.069 -0.331
23 -0.074 -0.019 -0.025 -0.070 57 -0.186 -0.067 -0.104 -0.218
24 -0.119 -0.035 -0.025 -0.051 58 -0.037 -0.124 -0.038 -0.086
25 -0.165 -0.056 -0.113 -0.326 59 -0.250 -0.109 -0.168 -0.324
26 -0.097 -0.026 -0.054 -0.337 60 -0.109 -0.031 -0.083 -0.360
27 -0.034 -0.007 -0.039 -0.250 61 -0.020 -0.079 -0.038 -0.086
28 -0.272 -0.127 -0.158 -0.225 62 -0.069 -0.017 -0.050 -0.245
29 -0.114 -0.033 -0.066 -0.199 63 -0.045 -0.141 -0.047 -0.099
30 -0.213 -0.083 -0.128 -0.258 64 -0.208 -0.342 -0.332 -0.336
31 -0.326 -0.184 -0.233 -0.367 65 -0.092 -0.024 -0.042 -0.295
32 -0.288 -0.142 -0.202 -0.365 66 -0.056 -0.013 -0.047 -0.246
33 -0.084 -0.022 -0.063 -0.301 67 -0.036 -0.122 -0.070 -0.132
34 -0.119 -0.035 -0.054 -0.308 68 -0.134 -0.042 -0.071 -0.201
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58
Data µi1 µi2 µi3 µi4 Data µi1 µi2 µi3 µi4
69 -0.254 -0.363 -0.359 -0.348 85 -0.082 -0.021 -0.038 -0.118
70 -0.035 -0.119 -0.054 -0.111 86 -0.216 -0.085 -0.121 -0.354
71 -0.086 -0.022 -0.022 -0.197 87 -0.138 -0.043 -0.078 -0.356
72 -0.084 -0.214 -0.105 -0.176 88 -0.351 -0.225 -0.257 -0.287
73 -0.026 -0.096 -0.014 -0.039 89 -0.028 -0.102 -0.020 -0.051
74 -0.124 -0.037 -0.084 -0.331 90 -0.023 -0.088 -0.035 -0.078
75 -0.058 -0.168 -0.072 -0.136 91 -0.102 -0.028 -0.066 -0.235
76 -0.029 -0.104 -0.045 -0.096 92 -0.109 -0.031 -0.076 -0.283
77 -0.159 -0.053 -0.088 -0.197 93 -0.013 -0.057 -0.030 -0.070
78 -0.097 -0.233 -0.146 -0.217 94 -0.098 -0.027 -0.060 -0.240
79 -0.357 -0.333 0.000 0.000 95 -0.198 -0.074 -0.103 -0.204
80 -0.318 -0.174 -0.231 -0.365 96 -0.023 -0.087 -0.041 -0.089
81 -0.125 -0.038 -0.079 -0.243 97 -0.031 -0.109 -0.044 -0.095
82 -0.066 -0.016 -0.032 -0.121 98 -0.146 -0.047 -0.050 -0.099
83 -0.023 -0.086 -0.028 -0.067 99 -0.016 -0.065 -0.007 -0.022
84 -0.015 -0.064 -0.040 -0.087 100 -0.113 -0.033 -0.057 -0.161
Below is the calculation of the PEI value:
PEI = -
= 0.546967522
The value of the PEI (Partition Entropy Index) is 0.546967522.
4.3.3 Fuzzy Subtractive Clustering Processing
The determination of the number of clusters is still the same as the Fuzzy C-Means
method based on 10 (ten) main variables, both of categories include data Tx Power, Rx
Power, Temperature, Power Supply, and Bias Current. The data can be seen in Table
4.1. The parameters used in the process of clustering using the Fuzzy Subtractive
Clustering algorithm are:
Influence range (r) = 0.2;
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59
Accept ratio = 0.5;
Reject ratio = 0.15;
Squash factor (q) = 1.25;
Bottom line (Xmin) = [0;0;0;0;0;0;0;0;0;0]
Upper limit (Xmax) = [5;100;70;5;25;5;5;70;5;50]
The first step in the grouping process with Fuzzy Subtractive Clustering is the
normalization of data is to equalize the range between the 10 variables. Normalization
of data can be calculated using the following Equation 2.6. Example on the first data:
First Variable
X11 =
=
= 0.462
Second Variable
X12 =
=
= -0.2409
Third Variable
X13 =
=
= 0.714285714
Fourth Variable
X14 =
=
= 0.668
Fifth Variable
X15 =
=
= 0.68
Sixth Variable
X16 =
=
= 0.74
Seventh Variable
X17 =
=
= -0.13882
Eight Variable
X18 =
=
= 0.528571429
Ninth Variable
X19 =
=
= 0.648
Tenth Variable
X110 =
=
= 0.68
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60
The above step is also done to the 2nd data up to the 100th data. So the final result of normalization as in Table 4.6.
Tabel 4.6 Normalization Data
No
ONU - Optical Network Unit (from Customer) OLT - Optical Network Termination (from Company)
Tx
Power
(dBm)
Rx
Power
(dBm)
Temperature
(ᵒC)
Power
Supply
(Volt)
Bias
Current
(mA)
Tx
Power
(dBm)
Rx
Power
(dBm)
Temperature
(ᵒC)
Power
Supply
(Volt)
Bias
Current
(mA)
1 0.462 -0.2409 0.714286 0.668 0.68 0.74 -2.7764 0.528571 0.648 0.3
2 0.5372 -0.15392 0.5563 0.656 0.514 0.57 -2.8272 0.614286 0.627 0.61356
3 0.42 -0.1928 0.6 0.648 0.52 0.734 -2.6648 0.628571 0.64 0.34
4 0.47 -0.1703 0.571429 0.652 0.44 0.772 -2.5508 0.6 0.636 0.2
5 0.448 -0.173 0.714286 0.648 0.44 0.734 -2.5344 0.728571 0.642 0.26
6 0.4216 -0.20088 0.791186 0.644 0.644 0 -3.8292 0 0 0
7 0.396 -0.3154 0.6 0.656 0.48 0.81 -3.1208 0.5 0.638 0.16
8 0.386 -0.3397 0.614286 0.652 0.4 0.752 -3.1592 0.528571 0.652 0.28
9 0.404 -0.1549 0.571429 0.656 0.48 0.698 -2.4368 0.685714 0.64 0.24
10 0.41 -0.2125 0.685714 0.656 0.48 0.682 -2.7136 0.685714 0.638 0.22
11 0.46 -0.1815 0.671429 0.656 0.56 0.758 -2.5836 0.457143 0.664 0.22
12 0.456 -0.1866 0.6 0.648 0.4 0.722 -2.5088 0.671429 0.634 0.34
13 0.416 -0.1673 0.714286 0.66 0.32 0.73 -2.552 0.314286 0.64 0.18
14 0.436 -0.1705 0.642857 0.656 0.28 0.762 -2.5804 0.314286 0.64 0.18
15 0.454 -0.1958 0.614286 0.664 0.52 0.734 -2.7064 0.728571 0.638 0.36
16 0.404 -0.1889 0.8 0.656 0.4 0.78 -2.6324 0.471429 0.64 0.18
17 0.462 -0.2081 0.671429 0.652 0.48 0.768 -2.692 0.571429 0.646 0.22
18 0.4 -0.1632 0.742857 0.656 0.36 0.802 -2.5228 0.557143 0.642 0.18
19 0.5112 -0.20758 0.734371 0.636 0.84592 0.7028 -4.3242 0.642857 0.6284 0.59288
Page 74
61
No
ONU - Optical Network Unit (from Customer) OLT - Optical Network Termination (from Company)
Tx
Power
(dBm)
Rx
Power
(dBm)
Temperature
(ᵒC)
Power
Supply
(Volt)
Bias
Current
(mA)
Tx
Power
(dBm)
Rx
Power
(dBm)
Temperature
(ᵒC)
Power
Supply
(Volt)
Bias
Current
(mA)
20 0.474 -0.2468 0.642857 0.66 0.52 0.82 -2.9296 0.5 0.634 0.18
21 0.456 -0.1655 0.642857 0.636 0.32 0.714 -2.5804 0.6 0.642 0.22
22 0.424 -0.1798 0.585714 0.648 0.32 0.816 -2.6368 0.685714 0.634 0.26
23 0.45 -0.1754 0.685714 0.648 0.44 0.734 -2.5672 0.514286 0.648 0.26
24 0.42 -0.1946 0.671429 0.648 0.4 0.786 -2.6244 0.5 0.636 0.2
25 0.484 -0.1947 0.611 0.648 0.488 0.692 -4.3254 0.558571 0.6424 0.24428
26 0.47 -0.1623 0.728571 0.66 0.32 0.736 -2.554 0.642857 0.642 0.34
27 0.398 -0.1879 0.642857 0.656 0.44 0.752 -2.6148 0.571429 0.646 0.22
28 0.428 -0.1807 0.7 0.652 0.32 0.74 -2.5876 0.414286 0.648 0.3
29 0.406 -0.1841 0.757143 0.656 0.36 0.726 -2.5868 0.528571 0.66 0.26
30 0.432 -0.2284 0.757143 0.656 0.72 0.75 -2.8372 0.514286 0.646 0.22
31 0.5164 -0.138 0.765843 0.644 0.772 0.6496 -3.016 0.842857 0.6296 0.82962
32 0.462 -0.19706 0.760771 0.644 0.716 0.7296 -4.1786 0.587214 0.6 0.60028
33 0.446 -0.1979 0.642857 0.656 0.24 0.76 -2.6572 0.571429 0.64 0.22
34 0.448 -0.1614 0.685714 0.66 0.28 0.744 -2.5416 0.7 0.638 0.22
35 0.448 -0.1614 0.685714 0.66 0.28 0.744 -2.5416 0.7 0.638 0.22
36 0.436 -0.1832 0.642857 0.656 0.48 0.662 -2.5296 0.5 0.636 0.22
37 0.464 -0.1983 0.628571 0.664 0.4 0.696 -2.6432 0.6 0.64 0.14
38 0.372 -0.1886 0.614286 0.648 0.36 0.752 -2.6848 0.385714 0.634 0.28
39 0.47 -0.1809 0.657143 0.652 0.52 0.67 -2.5264 0.642857 0.636 0.22
40 0.404 -0.213 0.771429 0.652 0.4 0 -2.7876 0 0 0
41 0.456 -0.173 0.728571 0.66 0.32 0.732 -2.5308 0.471429 0.666 0.28
42 0.406 -0.1943 0.571429 0.64 0.36 0.746 -2.5228 0.657143 0.642 0.36
Page 75
62
No
ONU - Optical Network Unit (from Customer) OLT - Optical Network Termination (from Company)
Tx
Power
(dBm)
Rx
Power
(dBm)
Temperature
(ᵒC)
Power
Supply
(Volt)
Bias
Current
(mA)
Tx
Power
(dBm)
Rx
Power
(dBm)
Temperature
(ᵒC)
Power
Supply
(Volt)
Bias
Current
(mA)
43 0.43 -0.1798 0.657143 0.66 0.32 0.728 -2.6092 0.557143 0.636 0.18
44 0.4408 0.98064 0.636214 0.64 0.504 0.706 -4.2868 0.742857 0.6352 0.64708
45 0.47 -0.1939 0.714286 0.66 0.64 0.81 -2.5296 0.557143 0.642 0.16
46 0.444 -0.1917 0.742857 0.656 0.36 0.75 -2.6696 0.442857 0.64 0.2
47 0.408 -0.2194 0.714286 0.66 0.28 0.75 -2.7776 0.557143 0.656 0.3
48 0.438 -0.1809 0.9 0.656 0.4 0.728 -2.556 0.528571 0.642 0.14
49 0.454 -0.2657 0.628571 0.664 0.44 0.732 -2.798 0.685714 0.634 0.22
50 0.518 -0.2409 0.755743 0.636 0.56 0.7578 -4.6054 0.745243 0.6 0.58936
51 0.454 -0.2075 0.757143 0.656 0.36 0.684 -2.7436 0.785714 0.642 0.32
52 0.388 -0.1801 0.671429 0.652 0.48 0.75 -2.5672 0.528571 0.668 0.24
53 0.434 -0.1829 0.742857 0.656 0.32 0.78 -2.6348 0.742857 0.64 0.26
54 0.404 -0.1495 0.757143 0.656 0.4 0.746 -2.486 0.642857 0.646 0.32
55 0.458 -0.1818 0.714286 0.644 0.4 0.806 -2.5288 0.542857 0.642 0.18
56 0.452 -0.197 0.614286 0.656 0.44 0.79 -2.648 0.714286 0.644 0.18
57 0.432 -0.1785 0.771429 0.66 0.28 0.738 -2.5776 0.5 0.66 0.22
58 0.5224 -0.23098 0.666514 0.64 0.644 0 -3.4244 0 0 0
59 0.432 -0.2125 0.514286 0.656 0.28 0.792 -2.7276 0.528571 0.642 0.14
60 0.476 -0.1365 0.671429 0.664 0.56 0.822 -2.4796 0.614286 0.638 0.16
61 0.4268 -0.18014 0.687171 0.64 0.388 0 -3.5496 0 0 0
62 0.442 -0.2097 0.657143 0.66 0.56 0.738 -2.6672 0.571429 0.632 0.2
63 0.646 -0.2398 0.779629 0.652 0.67464 0 -3.4428 0 0 0
64 0.4952 0.13316 0.837171 0.66 0.546 0 -4.7924 0 0 0
65 0.462 -0.1534 0.671429 0.66 0.56 0.736 -2.486 0.671429 0.642 0.24
Page 76
63
No
ONU - Optical Network Unit (from Customer) OLT - Optical Network Termination (from Company)
Tx
Power
(dBm)
Rx
Power
(dBm)
Temperature
(ᵒC)
Power
Supply
(Volt)
Bias
Current
(mA)
Tx
Power
(dBm)
Rx
Power
(dBm)
Temperature
(ᵒC)
Power
Supply
(Volt)
Bias
Current
(mA)
66 0.45 -0.1913 0.657143 0.664 0.56 0.732 -2.6548 0.571429 0.632 0.2
67 0.4788 -0.1824 0.629129 0.64 0.548 0 -2.9844 0 0 0
68 0.468 -0.2337 0.657143 0.656 0.52 0.74 -2.7824 0.542857 0.64 0.16
69 0.5176 0.2222 0.595814 0.64 0.502 0 -3.398 0 0 0
70 0.578 -0.1947 0.760771 0.64 0.776 0 -2.9868 0 0 0
71 0.428 -0.1939 0.685714 0.648 0.48 0.738 -2.6108 0.685714 0.642 0.24
72 0.41 -0.28862 0.646314 0.64 0.556 0 -3.56 0 0 0
73 0.5008 -0.22758 0.720257 0.64 0.642 0 -4.1408 0 0 0
74 0.414 -0.2244 0.628571 0.656 0.52 0.712 -2.798 0.6 0.64 0.14
75 0.4728 -0.24814 0.6683 0.656 0.376 0 -4.536 0 0 0
76 0.4676 -0.18762 0.730414 0.64 0.674 0 -5.2044 0 0 0
77 0.466 -0.1578 0.7 0.66 0.6 0.72 -2.5428 0.514286 0.64 0.16
78 0.6368 -0.24684 0.900229 0.656 0.67632 0 -3.4112 0 0 0
79 0.4356 0.98064 0.636214 0.64 0.498 0.6946 -4.2814 0.742857 0.6346 0.64472
80 0.432 -0.1634 0.671429 0.648 0.44 0.734 2.5628 0.657143 0.642 0.18
81 0.426 -0.185 0.6 0.652 0.32 0.738 -2.5984 0.528571 0.638 0.22
82 0.454 -0.205 0.685714 0.648 0.56 0.75 -2.6456 0.542857 0.664 0.24
83 0.684 -0.19788 0.728743 0.664 0.45584 0 -4.7536 0 0 0
84 0.5076 -0.15592 0.684829 0.644 0.662 0 -4.6024 0 0 0
85 0.43 -0.1844 0.671429 0.656 0.36 0.746 -2.692 0.514286 0.656 0.28
86 0.388 -0.1882 0.771429 0.652 0.2 0.684 -2.688 0.8 0.642 0.34
87 0.404 -0.1863 0.785714 0.636 0.4 0.722 -2.5952 0.685714 0.632 0.24
88 0.464 -0.2796 0.685714 0.656 0.44 0.76 -3.062 0.4 0.64 0.12
Page 77
64
No
ONU - Optical Network Unit (from Customer) OLT - Optical Network Termination (from Company)
Tx
Power
(dBm)
Rx
Power
(dBm)
Temperature
(ᵒC)
Power
Supply
(Volt)
Bias
Current
(mA)
Tx
Power
(dBm)
Rx
Power
(dBm)
Temperature
(ᵒC)
Power
Supply
(Volt)
Bias
Current
(mA)
89 0.4344 -0.22678 0.745586 0.644 0.676 0 -3.7788 0 0 0
90 0.6404 -0.18664 0.757029 0.656 0.55848 0 -4.978 0 0 0
91 0.456 -0.1939 0.757143 0.66 0.36 0.746 -2.704 0.542857 0.652 0.28
92 0.404 -0.1737 0.742857 0.648 0.28 0.774 -2.5508 0.571429 0.64 0.18
93 0.5004 -0.16576 0.676614 0.644 0.666 0 -4.31 0 0 0
94 0.466 -0.2346 0.642857 0.64 0.36 0.764 -2.7468 0.557143 0.646 0.22
95 0.442 -0.2495 0.642857 0.66 0.52 0.794 -2.9684 0.5 0.634 0.18
96 0.4688 -0.18182 0.6413 0.644 0.554 0 -4.348 0 0 0
97 0.4936 -0.20058 0.794314 0.66 0.40856 0 -3.842 0 0 0
98 0.434 -0.1899 0.714286 0.648 0.52 0.766 -2.5368 0.5 0.644 0.18
99 0.548 -0.20606 0.7 0.636 0.634 0 -4.104 0 0 0
100 0.446 -0.1869 0.742857 0.656 0.4 0.728 -2.5836 0.514286 0.656 0.28
After obtaining the normalized data, the next step is to determine the initial potential value of the 1st data until the 100th data then search for
data with the largest potential value selected as the first group center. The initial potential of each data is calculated using the Equation 2.8 and
the calculation results are presented in Table 4.7.
Page 78
65
Table 4.7 Inital Potential
Data Initial Potential Data Initial Potential
1 3.276159146 42 3.05581125
2 1.000310815 43 10.00685708
3 4.1270792 44 1.98294683
4 6.190572893 45 5.179353148
5 5.851388426 46 6.667127884
6 3.313221293 47 0
7 2.659123335 48 1.428574518
8 1.936308772 49 4.913351358
9 3.762197928 50 1.049349778
10 5.831236185 51 2.26617063
11 7.018811926 52 10.26778953
12 4.415836643 53 3.938108254
13 1.965670626 54 4.191252417
14 1.853361045 55 9.190336649
15 2.762023334 56 3.155739715
16 4.503353971 57 6.809755242
17 13.2673036 58 5.110787063
18 6.875952963 59 1.852572376
19 1.320020299 60 4.103295809
20 6.231248337 61 3.077395944
21 8.846517591 62 11.64060376
22 3.32240608 63 2.348530758
23 12.04167891 64 1.000761166
24 11.02598771 65 6.347572338
25 4.324908138 66 11.54631924
26 3.892154155 67 3.907034509
27 0.00000000 68 9.766880298
28 4.219938598 69 1.000715577
29 8.640826755 70 2.584350232
30 3.297782113 71 8.094687041
31 1.000037395 72 2.439496374
32 1.317543263 73 6.171326863
33 7.662633712 74 6.371475372
34 5.696934499 75 2.684113847
35 5.696934499 76 4.5960941
36 6.329872041 77 0
37 0 78 1.349290593
38 2.15731114 79 1.98294683
39 6.593156423 80 1.010341706
40 2.250267828 81 7.886066853
41 7.186045346 82 11.08180887
Page 79
66
Data Initial Potential Data Initial Potential
85 10.37810748 93 5.854686624
86 1.521320815 94 10.14108712
87 0 95 7.886706952
88 2.055603647 96 4.988301099
89 4.442336353 97 0
90 2.500674274 98 10.1518002
91 8.361222521 99 5.703634866
92 6.400144661 100 9.355512058
Based on Table 4.7 it can be seen that the data with the greatest initial potential
value is in the 23rd data selected as the first group center with 12.04167891.
Next, look for the point with the highest initial potential.
M = max [At | i = 1,2, ..., n] = 12.04167891 the potential in the 23rd data;
h = i = 3, such that D23 = M = 12.04167891;
After that, determine the center of the cluster and reduce its potential to the surrounding
points:
a) Center = []
b) C = 0
c) Conditions = 1
d) Z = M = 12.04167891
Due to Condition≠0 and Z≠0, then do the calculation for #1st
Iteration
a. Determine the center of the cluster:
The highest potential lies in the 23rd data, then the result of normalization of the
23rd data becomes the center of the cluster, namely: V1 = 0.45; V2 = -0.1754; V3 =
0.685714286; V4 = 0.648; V5 = 0.44; V6 = 0.734; V7 = -2.5672; V8 =
0.514285714; V9 = 0.648; V10 = 0.26
b. Determining whether a cluster center is accepted or not as a cluster center
Ratio = Z / M = 12.04167891 / 12.04167891 = 1
Ratio > accept_ratio (0.5), then Condition = 1.
Page 80
67
c. Condition = 1 means cluster center candidate accepted as a cluster center, then:
1) C = C + 1 = 1
2) Center1 = 0.45; -0.1754; 0.685714286; 0.648; 0.44; 0.734; -2.5672;
0.514285714; 0.648; 0.26
3) Reduce the potential of the points near the center of the cluster from the first data
up to the hundredth data.
Example on the first data:
The potential abatement value for the first data is:
Dc1 = M * e-4|ST1|
= 12.04167891 * 2.7187-4|1.408004|
= 3.54869605
The new potential value is calculated by subtracting the potential of the first data with
the first potential degradation value:
D1 = D1 – Dc1
= 3.276159146 - 3.54869605
= -0.272536904
The calculation results for the 2nd data until the hundredth data are presented in Table
4.8.
Table 4.8 New Potential
Data New Potential Data New Potential
D44 1.977449198 D63 1.260131
D79 1.977449198 D93 1.231021
D73 1.668210576 D78 1.209095
D99 1.644165223 D43 1.205291
D95 1.561545146 D96 1.196209
D6 1.525501475 D62 1.146511
D89 1.523932431 D7 1.125091
D20 1.412718284 D34 1.098794
Page 81
68
Data New Potential Data New Potential
D35 1.098794 D85 0.185429
D58 1.067294 D15 0.14628
D8 1.055217 D59 0.13181
D66 1.054353 D10 0.11719
D88 1.039186 D100 0.069958
D72 1.029713 D5 0.053118
D61 1.015042 D14 0.010086
D19 1.010005 D94 0.002433
D32 1.010005 D23 0
D90 1.00177 D97 -2.2E-20
D83 1.00177 D18 -0.06117
D75 1.000818 D22 -0.09818
D84 1.000618 D45 -0.13345
D67 1.000517 D46 -0.16963
D70 1.000359 D91 -0.19627
D40 1.000158 D52 -0.21235
D76 1.000072 D13 -0.24679
D64 1 D65 -0.33734
D50 1 D42 -0.34198
D69 1 D9 -0.41075
D25 1 D12 -0.42353
D80 1 D55 -0.48643
D31 0.999975 D41 -0.49802
D2 0.921618 D16 -0.53104
D30 0.848634 D60 -0.53183
D86 0.746032 D98 -0.5365
D29 0.652979 D26 -0.55793
D74 0.642866 D39 -0.63623
D17 0.631461 D48 -0.64122
D21 0.619483 D3 -0.69201
D24 0.546035 D28 -0.70052
D68 0.485935 D11 -0.81884
D92 0.472328 D38 -0.90043
D51 0.434219 D56 -0.93916
D82 0.417202 D4 -0.96054
D49 0.401231 D54 -0.97844
D1 0.397254 D47 -1.44198
D53 0.395333 D36 -1.65212
D57 0.385249 D87 -2.45806
D33 0.355057 D77 -2.77507
D71 0.306278 D37 -2.88816
D81 0.219735 D27 -4.1498
Page 82
69
Based on Table 4.8 it can be seen that the data with the greatest potential value is
in the 44th data with the potential value of 1.977449198. To determine the center of the
group so it will be used the value of the ratio.
To determine the next group center, done the same way. If the ratio ≤ reject ratio,
then there is no longer data that is considered to be a candidate for group center and
iteration stop. After that, seeking the point with the highest new potential:
a) Z = max [At | i = 1,2, ..., n] = 1.977449198 the potential on the 44th data
b) h = i = 44, such that D44 = Z = 1.977449198
Due to Condition ≠ 0 and Z ≠ 0, then do the calculation for #2nd Iteration with the
same step with the previous point c, so obtained:
Ratio = Z / M
= 1.977449198 / 12.04167891
= 0.39189028
Ratio ≤ reject_ratio (0,5), then Condition = 0
Condition = 0 means cluster center candidate is not accepted as cluster center,
then process is stopped with cluster number 44 and center of cluster as in Table 4.9.
Returns the cluster center of the normalized shape to its original shape which is
denormalization data. By using the Equation 2.10 the example of calculation for the
first data is:
1st Variable
Center11 = 0.462 * (5 – 0) + 0
= 2.31
2nd Variable
Center12 = -0.2409 * (100 – 0) + 0
= -24.09
3rd Variable
Page 83
70
Center13 = 0.714285714 * (70 – 0) + 0
= 50
4th Variable
Center14 = 0.668 * (50 – 0) + 0
= 3.34
5th Variable
Center15 = 0.34 * (50 – 0) + 0
= 17
6th Variable
Center16 = 0.74 * (5 – 0) + 0
= 3.72.31
7th Variable
Center17 = -0.13882 * (100 – 0) + 0
= -13.882
8th Variable
Center18 = 0.528571429 * (70 – 0) + 0
= 37
9th Variable
Center19 = 0.648 * (50 – 0) + 0
= 3.24
10th Variable
Center110 = 0.3 * (50 – 0) + 0
= 15
Table 4.9 Normalization and Denormalization Data
23th
Data NORMALIZATION
Tx Power (dBm) 0.45
Rx Power (dBm) -0.1754
Temperature (ᵒC) 0.685714
Power Supply (Volt) 0.648
Bias Current (mA) 0.44
Tx Power (dBm) 0.734
Rx Power (dBm) -2.5672
Temperature (ᵒC) 0.514286
Power Supply (Volt) 0.648
Bias Current (mA) 0.26
Page 84
71
DENORMALIZATION
Tx Power (dBm) 2.25
Rx Power (dBm) -17.54
Temperature (ᵒC) 48
Power Supply (Volt) 3.24
Bias Current (mA) 11
Tx Power (dBm) 3.67
Rx Power (dBm) -12.836
Temperature (ᵒC) 36
Power Supply (Volt) 3.24
Bias Current (mA) 13
At the last iteration obtained the sigma value. By using the Equation 2.11 the
example of calculation for the first variable is:
σ1 = 0.2 *
√
= 0.353553391
Do the calculations also on the second variable to the tenth variable. More data is
shown in Table 4.10.
Table 4.10 Sigma Cluster
By using the Gauss function in Equation 2.12, it can be found the degree of
membership of each data in each group. The degree of membership of the 1st data (i =
1,2, ..., 100) in cluster 1:
Variable Sigma Value
v1 0.353553391
v2 7.071067812
v3 4.949747468
v4 0.353553391
v5 1.767766953
v6 0.353553391
v7 0.353553391
v8 4.949747468
v9 0.353553391
v10 3.535533906
Page 85
72
µ11 = (
) (
) (
)
= 0.110802385
The above step is also done to the second until the hundredth data so that the
final result of degree of membership for all data such as in Table 4.11.
Table 4.11 Degree of Membership using Radius 0.2
Data
Degree of Membership
Data
Degree of Membership
On the cluster On the cluster
1 1
1 0.110802385 32 1.81308E-07
2 6.34438E-09 33 0.164498458
3 0.051309787 34 0.013520565
4 0.073985617 35 0.013520565
5 0.009294668 36 0.379341254
6 5.91087E-58 37 0.061353105
7 0.008939101 38 0.04761789
8 0.021431848 39 0.080159648
9 0.008869171 40 2.80375E-57
10 0.024027056 41 0.440848421
11 0.378959092 42 0.008555742
12 0.019544169 43 0.261823904
13 0.005373631 44 4.61368E-68
14 0.00378421 45 0.05310498
15 0.001754273 46 0.239805972
16 0.072433696 47 0.224748526
17 0.453953034 48 0.00219121
18 0.128995092 49 0.013551849
19 9.3301E-09 50 4.30385E-09
20 0.092744111 51 0.000155328
21 0.220951534 52 0.562915739
22 0.006335905 53 0.002095867
23 1 54 0.056994833
24 0.426007517 55 0.252150299
25 0.143437117 56 0.004003877
26 0.054348446 57 0.198118473
27 0.36935556 58 1.07457E-57
28 0.202519074 59 0.003840869
29 0.39888693 60 0.033000004
30 0.050080224 61 6.05455E-57
31 1.39807E-21 62 0.273538673
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Data
Degree of Membership
Data
Degree of Membership
On the cluster On the cluster
1 1
63 1.07202E-59 82 0.536019202
64 1.1422E-62 83 9E-60
65 0.051167829 84 6.27105E-58
66 0.299104369 85 0.741113182
67 4.1488E-57 86 8.82792E-06
68 0.17843479 87 0.013611333
69 2.56422E-64 88 0.010964492
70 5.28947E-59 89 7.90248E-58
71 0.044731571 90 2.2723E-59
72 9.86142E-58 91 0.421160916
73 8.84402E-58 92 0.099120652
74 0.044804726 93 8.7192E-58
75 1.6211E-57 94 0.310902793
76 3.05028E-58 95 0.136176561
77 0.172469822 96 2.26218E-57
78 3.32217E-61 97 1.3419E-57
79 5.17287E-68 98 0.348925497
80 0 99 6.3879E-58
81 0.257854089 100 0.645440111
4.3.4 Fuzzy Subtractive Clustering Validation
Next, do the clustering validity on Fuzzy Subtractive Clustering method with 2
indicators as follows.
a. Partition Coefficient Index (PCI)
To calculate the value of PCI, the Equation 2.13 is employed. Below is the result of PCI
validation on Fuzzy Subtractive Clustering method as shown in Table 4.12.
Table 4.12 PCI Result on Fuzzy Subtractive Clustering
Data µi12 Data µi1
2
1 3.50711E-10 3 0.000150712
2 2.46075E-23 4 0.005187898
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Data µi12 Data µi1
2
5 6.97036E-05 48 3.68357E-06
6 6.9631E-256 49 4.45358E-09
7 1.75794E-31 50 0
8 1.55982E-34 51 1.86016E-11
9 2.08097E-06 52 0.249262018
10 6.31221E-06 53 2.03573E-07
11 0.015696594 54 0.000685762
12 0.000152162 55 0.037267464
13 3.18011E-06 56 4.35821E-06
14 2.97278E-07 57 0.000825635
15 2.46857E-08 58 4.8728E-181
16 0.001767393 59 1.87083E-09
17 0.007250074 60 2.71696E-05
18 0.004299536 61 5.8778E-197
19 5.4774E-295 62 0.001173664
20 1.37614E-14 63 1.1162E-188
21 0.005437778 64 0
22 1.76131E-06 65 8.10309E-05
23 1 66 0.002232037
24 0.074323458 67 2.486E-129
25 2.1401E-270 68 1.18459E-06
26 0.000329004 69 5.8194E-188
27 0.086812022 70 6.8834E-140
28 0.004353103 71 0.001077197
29 0.056427735 72 5.1606E-201
30 9.45901E-15 73 0
31 4.56146E-67 74 1.86396E-08
32 3.7983E-244 75 0
33 1.33278E-05 76 0
34 3.4476E-06 77 0.000567744
35 3.4476E-06 78 4.8606E-187
36 0.085376596 79 0
37 0.000935405 80 0
38 5.50026E-05 81 0.00631439
39 0.001765069 82 0.009721559
40 3.824E-118 83 0
41 0.017207019 84 0
42 1.89143E-05 85 0.009405842
43 0.005560405 86 7.50033E-16
44 0 87 0.000124636
45 5.27246E-06 88 7.37453E-26
46 0.002718271 89 9.5362E-246
47 1.58574E-07 90 0
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Data µi12 Data µi1
2
91 0.001623824 96 0
92 0.00020014 97 2.4448E-255
93 0 98 0.038767864
94 5.9374E-05 99 0
95 8.04084E-17 100 0.310583273
Below is the calculation of the PCI value:
PCI =
= 0.020459432
The value of the PCI (Partition Coefficient Index) is 0.020459432.
b. Partition Entropy Index (PEI)
To calculate the value of PEI, the Equation 2.14 is employed. Below is the result of PEI
validation on Fuzzy Subtractive Clustering method as shown in Table 4.13.
Table 4.13 PEI Result on Fuzzy Subtractive Clustering
Data µi1 Data µi1
1 -0.000203856 18 -0.17865591
2 -1.29122E-10 19 -2.5073E-145
3 -0.054017443 20 -1.87207E-06
4 -0.18948256 21 -0.192257736
5 -0.039954585 22 -0.008791954
6 -7.7517E-126 23 0
7 -1.48458E-14 24 -0.354318765
8 -4.86103E-16 25 -4.5418E-133
9 -0.009436246 26 -0.072730216
10 -0.015040579 27 -0.36005011
11 -0.260238637 28 -0.17935692
12 -0.054217582 29 -0.341446855
13 -0.011286947 30 -1.57031E-06
14 -0.004097039 31 -5.15845E-32
15 -0.001376111 32 -5.4618E-120
16 -0.133231186 33 -0.020490904
17 -0.209749625 34 -0.011677085
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Data µi1 Data µi1
35 -0.011677085 68 -0.007426129
36 -0.35949689 69 -5.20012E-92
37 -0.106655892 70 -4.20347E-68
38 -0.036370372 71 -0.112138299
39 -0.133171197 72 -1.65649E-98
40 -2.64351E-57 73 -8.455E-164
41 -0.266446218 74 -0.001214952
42 -0.023649295 75 -7.4348E-223
43 -0.193581997 76 0
44 -1.2114E-193 77 -0.089040997
45 -0.013952772 78 -1.49546E-91
46 -0.154006536 79 -9.0809E-193
47 -0.003117424 80 0
48 -0.012006554 81 -0.20123738
49 -0.000641643 82 -0.228422365
50 -6.8691E-187 83 -4.1752E-264
51 -5.32817E-05 84 -3.1228E-236
52 -0.346799664 85 -0.226283592
53 -0.003475799 86 -4.76891E-07
54 -0.095386072 87 -0.050183034
55 -0.317528409 88 -7.8575E-12
56 -0.012884299 89 -8.7111E-121
57 -0.101995983 90 0
58 -1.44911E-88 91 -0.129412273
59 -0.000434627 92 -0.060241799
60 -0.027400316 93 -2.1765E-188
61 -1.73205E-96 94 -0.037493404
62 -0.115582707 95 -1.66157E-07
63 -2.28615E-92 96 -1.5885E-192
64 -9.8221E-275 97 -1.4494E-125
65 -0.042401148 98 -0.319971403
66 -0.144209892 99 0
67 -7.38231E-63 100 -0.325826334
Below is the calculation of the PEI value:
PEI = -
= 0.07013931
The value of the PEI (Partition Entropy Index) is 0.07013931.
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CHAPTER V
DISCUSSION
5.1 Grouping System Quality with Fuzzy C-Means Method
Conceptually, there are two algorithms in grouping techniques which are supervised and
unsupervised. The difference between the two lies in determining the number of clusters
that are formed. For supervised algorithms, it is necessary to know in advance the
number of clusters to be formed, where the method usually used is Fuzzy C-means
(FCM). The output of FCM is basically not a fuzzy inference system (IF-THEN) but is
a collection of cluster centers as well as some degree of membership for each data point,
then that information can be used to build a fuzzy inference system. FCM uses a fuzzy
grouping model so that data can be a member of all classes or clusters formed with
different degrees or membership levels between 0 and 1. The level of data presented in
a class or cluster is determined by the degree of membership. The FCM method requires
a large number of pre-defined group and group membership matrices. Typically, initial
group membership matrices are randomly initialized which causes the FCM method to
have inconsistency issues. The Fuzzy C-Means algorithm is one of the easiest and often
used algorithms in data grouping techniques because it makes efficient estimates and
does not require any parameters.
Based on the results of this study, it can be concluded for the grouping by Fuzzy
C-Means method there are several things related to the results of the system quality
classification based on 10 variables and 100 data. In accordance with the results
obtained, the researchers concluded by grouping into 4 groups of quality based on the
level of excellent quality, good quality, poor quality, very poor quality. The distribution
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of its cluster can be seen in Table 4.3. Several factors or strong variables that affect the
quality of the system on IndiHome still needs further investigation. Because in this
study, the final results obtained only to get the distribution of data to each cluster and
look for the degree of membership to be done on the next validity research. And not yet
known exactly which variables that affect grouping group. Thus, after getting the results
of clustering it should be identified the solution to treat the good quality system always
be in control to maintain the customer loyalty.
Cluster 1 consists of 5 factors in the ONU namely Tx Power with the data in the
range of 2.02 to 3.42 dBm, the data range in Rx Power is -28.862 to 22.22 dBm,
temperature from 41.707 to 63.016 ᵒC, power supply from 3.18 to 3.32 volt, bias current
from 9.4 to 19.4 mA. Then the 5 factors in the ONT are Tx Power with the data on the
entire cluster member is 0 dBm, the data range in Rx Power is -26,022 to -13,938 dBm,
the temperature with the data on the whole cluster member is 0, the power supply with
the data on the entire cluster member is 0 volt, the bias current with the data on all
cluster members is 0 mA. A significant difference in cluster 1 with the other 3 clusters
is that the characteristics of this cluster lie in the Tx Power, Temperature, Power
Supply, and Bias Current factors in the ONT. The data contained in these factors only
have the data that is 0 dBm. Then in Tx Power in ONU, cluster 1 has higher data up to
3.42 dBm.
In cluster 2 consists of 5 factors in the ONU namely Tx Power with the data in the
range of 1.94 to 2.686 dBm, the data range in Rx Power is -26.57 to 98.064 dBm,
temperature from 38.941 to 55 ᵒC, power supply from 3.18 to 3.32 volt, bias current
from 5 to 21.148 mA. Then the 5 factors in the ONT are Tx Power with the data in the
range of 2.85 to 4.08 dBm, the data range in Rx Power is -23.027 to 12.814 dBm,
temperature from 41.105 to 59 ᵒC, power supply from 3 to 3.23 volt, bias current from 9
to 41.481 mA. In the 2nd cluster, the characteristics that show significant differences
from this cluster are the Temperature and Bias Current factors in the ONT, the data
obtained has a higher yield than the other 3 clusters. In the Temperature factor, the data
goes to 59ᵒC and the data on the current bias has data up to 41,481 mA. Then in the
Power Rx factor at ONU, it has very high data which is 98,064 dBm.
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In cluster 3 consists of 5 factors in the ONU namely Tx Power with the data in the
range of 1.86 to 2.33 dBm, the data range in Rx Power is -27.96 to -15.78 dBm,
temperature from 43 to 63 ᵒC, power supply from 3.22 to 3.34 volt, bias current from 7
to 18 mA. Then the 5 factors in the ONT are Tx Power with the data in the range of
3.31 to 4.03 dBm, the data range in Rx Power is -15.31 to -12.614 dBm, temperature
from 22 to 40 ᵒC, power supply from 3.17 to 3.33 volt, bias current from 6 to 15 mA.
In clusters 3 and 4 have almost identical data on their characteristics, but the significant
difference between the two clusters is that cluster 3 has a larger than the cluster 4 on the
5 factors in the ONU.
In cluster 4 consists of 5 factors in the ONU namely Tx Power with the data in the
range of 1.93 to 2.42 dBm, the data range in Rx Power is -33.97 to -13.65 dBm,
temperature from 36 to 50 ᵒC, power supply from 3.18 to 3.32 volt, bias current from 6
to 16 mA. Then the 5 factors in the ONT are Tx Power with the data in the range of
3.46 to 4.11 dBm, the data range in Rx Power is -21.627 to -12.398 dBm, temperature
from 35 to 43 ᵒC, power supply from 3.16 to 3.34 volt, bias current from 7 to 14 mA.
However, on the ONT factor, cluster 4 has greater data from cluster 3.
In cluster 1, the available data that have unstable data marked by the number 0.
For clusters 2, 3 and 4, there are differences that are not too significant and none with
the problem of unstable data. However, with the limitations of this research, the
researcher did not carry out the analysis until it goes to the IF-THEN rule stage, so there
was no consideration of the final rule towards what type of quality existed in each
cluster. On the other hand, according to the parameter of validity clustering, Fuzzy C-
Means are better than the Fuzzy Subtractive Clustering in Partition Coefficient Index
(PCI) because the result is higher. Based on this case study, this method is better in
terms of measuring the amount of overlap among groups and evaluating the degree of
membership without considering the vector data.
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5.2 Grouping System Quality with Fuzzy Subtractive Clustering Method
Fuzzy subtractive clustering is an unsupervised clustering algorithm that can form the
number and center of the cluster corresponding to the data conditions. Fuzzy subtractive
clustering is based on density size or potential data points in a space or variable. The
basic concept of fuzzy subtractive clustering is to determine the regions in a variable
that has high density to the points around it. In contrast to the supervised algorithm,
grouping on an unsupervised algorithm cannot determine the number of clusters first,
where the method usually used is the subtractive clustering method (Kusumadewi &
Purnomo, 2004). FSC method has advantages in learning abilities that can solve
complex problems without formulating. Data processing in forming estimation models
based on subtractive grouping has special parameters in forming the number of clusters
which is radius parameters (influence range). Used radius is usually in the range of 0 to
1. The higher the radius used will produce a small number of clusters, and vice versa.
In this research using the subtractive clustering process, the cluster radius is from
0.1 until 1. For each radius have each number of clusters but when in radius 0.1 the
number of the cluster formed is 41 and then for radius 0.2 to 1, clusters formed only
one. It can be seen in Table 5.1. The ratio of acceptance and rejectance is a constant
value between 0 and 1 which is used as a measure for accepting and rejecting a cluster
central candidate data point into a cluster center. It is considering the accept ratio 0.5,
reject ratio 0.15, and squash factor 1.25. Similarly, at the center of different clusters,
although with the same number of clusters as this will certainly affect the degree of
membership. The grouping method that uses the fuzzy concept is a concept that a data
can be a member in all clusters with the degree of membership value it has. The higher
the degree of membership in a cluster, the greater the tendency to be a cluster member.
The value of its influence range close to 0 will affect the accuracy of the predicted data
and the number of clusters. There is a cluster central equilibrium of radius 0.2 to 0.8
because the cluster center of the radius is determined by the iteration process to locate
the points with the largest number of neighbors and on the radius having the same
number of iterations.
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Table 5.1 Number of Cluster
Radius Number of Clusters Formed Cluster Center
0.1 41 34
0.2 1 23
0.3 1 23
0.4 1 23
0.5 1 23
0.6 1 23
0.7 1 23
0.8 1 23
0.9 1 17
1 1 17
According to the parameter of validity clustering, Fuzzy Subtractive Clustering is
better than the Fuzzy C-Means in Partition Entropy Index (PEI) because the result is
smaller. This method is better to evaluate the randomness of the data in a cluster. But in
this case, after getting the number of clusters in each radius. It can be said that the
Fuzzy Subtractive Clustering method cannot be used by the company because the
results of the number of clusters obtained cannot represent the concept of the fuzzy
clustering. There are very far results when the number of clusters is 41 in the radius of
0.1 but after that it drops dramatically at a radius of 0.2 and so on with the number of
clusters only 1. Then, the number of clusters is 1 cannot enter the concept of clustering
itself, because clustering can be said to reach its destination if there is more than 1
cluster.
5.3 Sensitivity Analysis on Fuzzy Subtractive Clustering
The clustering process in the fuzzy clustering algorithm always finds the best solution
for defined parameters. However, this best solution may not necessarily determine the
best description of the data structure. To determine the most optimal number of clusters
and can validate whether fuzzy partitions applied in the clustering process are in
accordance with the data, the validity measurement index is used. The cluster validity
means the procedure to evaluate the results of the cluster analysis quantitatively so that
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the optimum group is produced. An optimum group is a group that has a solid range
between individuals in the group and is isolated from other groups well. In fuzzy
subtractive clustering, if the higher or lower radius is used it cannot promise good
estimation results, which is calculated based on several parameters of clustering validity
testing such as PCI and PEI. On testing the influence of the radius value is used finger
value 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1 with the value reject ratio is taken from
the best value on the previous test is 0.15 and the value accept ratio is equal to 0.5. test
result the influence of the radius values is shown in Table 5.2 and Figure 5.1
Table 5.2 PCI and PEI value
Radius PCI PEI
0.1 0.436662 0.074157
0.2 0.020459 0.070139
0.3 0.059397 0.155595
0.4 0.124276 0.192753
0.5 0.197615 0.193938
0.6 0.266852 0.180695
0.7 0.327196 0.163564
0.8 0.378117 0.14654
0.9 0.413066 0.139047
1 0.451738 0.123053
From the results obtained in Table 5.2, PCI results are used to measure the
number of overlap clusters and the highest results are in radius 1 with the value of
0.451738. It shows that with the largest PCI value, the cluster is the most optimal. Then
in PEI, it is necessary to see the degree of fuzziness of the resulting cluster partition.
The smallest PEI results show that the radius has an optimal number of clusters. The
smallest is in radius 0.2 with the value of 0.070139.
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Figure 5.1 Sensitivity Analysis based on PCI and PEI
In the PCI results there is a decrease in the radius of 0.1 to radius 0.2 but after that
it will increase again. This happens because the formula on the PCI is a quadratic result
of the degree of membership. In the result, in radius 0.1 there are 41 clusters, therefore
there is 41 degrees membership, and the radius of 0.2 to 1 has only 1 cluster, so there is
only 1 degree of membership, making the graph decrease from radius 0.1 to radius 0.2.
After that increase again because the higher the radius then the higher the PCI results
due to the results of squaring.
In PEI results there is a decrease as it goes to radius 0.2 and again rises at a radius
of 0.3 but an increase is only in a radius of 0.5 because after that the graph decreases
until heading to radius 1. The decrease in the graph from radius 0.1 to radius 0.2 due to
the differences number of clusters or the number of membership degrees significantly,
and then increased again because of the increasing radius that affects the calculation on
the PEI formula. However, when the graph is at a radius of 0.5 it decreases again as it
goes to a radius of 0.6 and so on, due to the result of different degrees of membership.
Then, when at a radius of 0.5 the result of membership degree is greater than the radius
of 0.6. Then at radius 0.9 and 1, having a different cluster center from the previous
radius and with the center of cluster 17 having fewer PEI results with that radius. Then
the graph will continue to decrease when the radius is at the point of radius 0.6 to radius
1.
0
0.1
0.2
0.3
0.4
0.5
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
RADIUS
SENSITIVITY ANALYSIS
PCI PEI
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CHAPTER VI
CONCLUSION AND RECOMMENDATION
6.1 CONCLUSION
After conducting the study, it can be concluded that:
1. For PCI, the better method is Fuzzy C-Means in measuring the amount of
overlapping among groups because it has the higher result. In Fuzzy C-Means
result, the value of the PCI (Partition Coefficient Index) is 0.662786731. It
shows that with the largest PCI value, the cluster is the most optimal. But in the
PEI result, Fuzzy Subtractive clustering is having the smallest value and it
becomes the better method especially to evaluate the randomness of the data in a
cluster. The smallest PEI is in radius 0.2 with the value of 0.070139. The
smallest PEI results show that the radius has an optimal number of clusters.
Then both methods can be said to be better with each parameter. But after
considering the number of clusters that are formed, compared to fuzzy c-means
method has 4 clusters and in fuzzy subtractive only two clustering numbers are
formed, which are 41 and 1. Then in the number of clusters parameter, the
method that can be used in terms of grouping quality is Fuzzy C-Means.
2. There is a change in the PCI indicator graph that experiencing the increases and
decreases. It occurs due to the formula that squaring the degree of membership
results. Similarly, sensitivity to the validity of PEI, the graphs are not
experiencing constant results, it can be said from the results of cluster validity
suffered significant sensitive changes.
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6.2 RECOMMENDATION
The advice given by the author to the PT. Telkom Indonesia branch Yogyakarta and
researchers for further research development as follows:
6.2.1 For PT. Telkom Indonesia branch Yogyakarta
1. The company can consider to cluster the quality to differentiate the treatment
carried out to the customer to reduce and overcome the complaint. Then in the
parameters of the number of the cluster formed, the company can use the Fuzzy
C-Means method. Besides to identify how many clusters are formed, they can
also see what kind of data will become the cluster members in each cluster and
find out the characteristics of each cluster to analyze the cluster types.
2. The company must focus and perform special treatment on cluster 1 because the
available data in the cluster has unstable data that marked 0. This also shows the
instability of the data, the system is categorized as bad quality.
6.2.2 For Further Researchers
1. To get the optimal result, it needs several times processes as comparisons. It
needs several times processes with different parameters.
2. A formal method in Fuzzy Subtractive Clustering is required to determine the
most optimal radius value in constructing estimation models.
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APPENDICES
Table Appendix 1. Fuzzy Subtractive Clustering Degree of Membership Radius 0.1
Data Degree of Membership (in cluster)
1 2 3 4 5 6 ... ... ... 37 38 39 40 41
1 1.2E-45 3.2E-08 6.6E-60 0 0 5.73E-14 ... ... ... 0 0 0 0 2.04E-12
2 3.5E-62 2.3E-44 4.2E-35 0 0 7.69E-52 ... ... ... 0 0 0 0 4.82E-26
3 2.2E-18 1.0E-05 2.9E-63 0 0 7.11E-23 ... ... ... 0 0 0 0 1
4 1.6E-09 1.2E-07 5.1E-61 0 0 6.87E-31 ... ... ... 0 0 0 0 1.46E-08
5 8.2E-06 4.6E-12 1.1E-57 0 0 1.99E-42 ... ... ... 0 0 0 0 4.09E-10
6 0 0 7.2E-28 0 0 0 ... ... ... 7.16E-36 9.1E-42 1.53E-44 3.04E-53 0
7 3.7E-80 1.5E-42 6.7E-22 0 0 1.22E-09 ... ... ... 2.4E-275 3.5E-28 0 0 2.36E-49
8 2.3E-82 1.4E-52 1.1E-12 0 0 4.02E-18 ... ... ... 2.9E-280 6.8E-28 0 0 4.02E-52
9 1.1E-12 6.0E-16 9.5E-56 0 0 1.31E-55 ... ... ... 0 0 0 0 5.19E-13
10 3.1E-14 2E-05 1.5E-65 0 0 6.29E-20 ... ... ... 0 0 0 0 2.49E-06
11 3.5E-25 9.2E-05 5.3E-64 0 0 3.84E-24 ... ... ... 0 0 0 0 3.73E-11
12 1.4E-07 1.9E-15 8.2E-55 0 0 3.07E-46 ... ... ... 0 0 0 0 4.88E-08
13 1.6E-27 1.3E-25 3.6E-44 0 0 2.04E-42 ... ... ... 0 0 0 0 6.64E-34
14 1.6E-27 1.2E-27 4.9E-41 0 0 9.19E-40 ... ... ... 0 0 0 0 3.57E-34
15 4.0E-20 2.1E-10 1.6E-58 0 0 4.87E-26 ... ... ... 0 0 0 0 0.004071
16 5.6E-17 2.2E-11 1.9E-56 0 0 1.01E-24 ... ... ... 0 0 0 0 1.6E-19
17 4.7E-15 0.0254 1.5E-65 0 0 6.58E-13 ... ... ... 0 0 0 0 1.21E-05
18 2.8E-07 4.3E-14 5.4E-54 0 0 1.84E-38 ... ... ... 0 0 0 0 1.36E-18
19 0 0 0 2.4E-27 3.1E-27 0 ... ... ... 0 0 1.5E-294 7.9E-305 0
20 8.0E-47 1.5E-15 2.7E-50 0 0 1 ... ... ... 9.8E-295 4.5E-29 0 0 7.11E-23
21 0.0013 7.0E-13 1.6E-57 0 0 3.85E-34 ... ... ... 0 0 0 0 2.52E-12
22 1.0E-05 5.7E-16 1.9E-51 0 0 1.76E-31 ... ... ... 0 0 0 0 9.87E-11
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Data Degree of Membership (in cluster)
1 2 3 4 5 6 ... ... ... 37 38 39 40 41
23 1.1E-11 1.3E-06 5.2E-63 0 0 1.89E-28 ... ... ... 0 0 0 0 2.27E-08
24 3.9E-12 5.7E-07 9.1E-61 0 0 7.93E-21 ... ... ... 0 0 0 0 3.79E-11
25 0 0 0 1.3E-27 2.3E-27 0 ... ... ... 0 0 1.1E-226 3.0E-221 0
26 0.00016 1.1E-18 4.7E-51 0 0 6.24E-44 ... ... ... 0 0 0 0 2.45E-13
27 7.0E-10 0.00026 2.7E-64 0 0 1.18E-22 ... ... ... 0 0 0 0 8.02E-06
28 7.2E-17 2.0E-18 8.6E-51 0 0 1.27E-34 ... ... ... 0 0 0 0 9.27E-19
29 5.3E-09 5.5E-12 1.1E-57 0 0 2.99E-32 ... ... ... 0 0 0 0 1.65E-13
30 2.9E-57 1.0E-12 8.2E-55 0 0 5.51E-13 ... ... ... 2E-297 9.2E-29 0 0 3.32E-22
31 1.3E-15 1.2E-11 9.8E-46 0 0 7.1E-117 ... ... ... 0 0 0 0 5.58E-91
32 0 0 0 3.5E-25 1.5E-25 0 ... ... ... 0 0 2.5E-283 2.6E-290 0
33 8.5E-07 9.2E-19 1.7E-49 0 0 1.38E-29 ... ... ... 0 0 0 0 5.4E-18
34 1 1.3E-20 7.2E-49 0 0 8.0E-47 ... ... ... 0 0 0 0 2.2E-18
35 1 1.3E-20 7.2E-49 0 0 8.04E-47 ... ... ... 0 0 0 0 2.2E-18
36 3.0E-16 2.9E-07 6.3E-66 0 0 2.27E-34 ... ... ... 0 0 0 0 7.58E-11
37 4.0E-09 1.3E-06 3.4E-64 0 0 1.24E-22 ... ... ... 0 0 0 0 3.53E-11
38 3.0E-25 3.8E-16 4.7E-52 0 0 5.89E-23 ... ... ... 0 0 0 0 1.29E-16
39 1.3E-12 1.6E-06 2.5E-66 0 0 1.67E-37 ... ... ... 0 0 0 0 2.47E-08
40 3.2E-27 6.7E-23 5.8E-51 0 0 2.3E-246 ... ... ... 1.03E-98 4.8E-94 0 0 1.6E-264
41 3.0E-11 3.5E-18 1.0E-51 0 0 5.52E-41 ... ... ... 0 0 0 0 5.11E-19
42 1.8E-08 1.1E-18 1.8E-50 0 0 4.86E-47 ... ... ... 0 0 0 0 4.22E-09
43 6.3E-06 1.2E-11 6.0E-58 0 0 1.07E-28 ... ... ... 0 0 0 0 3.41E-14
44 0 0 0 1 0.9128 0 ... ... ... 0 0 0 0 0
45 1.3E-28 4.1E-07 7.3E-61 0 0 4.6E-33 ... ... ... 0 0 0 0 1.19E-16
46 5.5E-17 6.4E-12 1.3E-56 0 0 7.79E-21 ... ... ... 0 0 0 0 2.83E-18
47 3.9E-16 3.8E-19 1.2E-48 0 0 1.59E-20 ... ... ... 0 0 0 0 1.23E-16
48 1.3E-17 1.0E-18 4.1E-51 0 0 7.61E-42 ... ... ... 0 0 0 0 1.05E-29
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Data Degree of Membership (in cluster)
1 2 3 4 5 6 ... ... ... 37 38 39 40 41
49 4.0E-19 2.9E-09 7.2E-59 0 0 1.25E-12 ... ... ... 0 0 0 0 2.63E-09
50 0 0 0 6.7E-28 6.1E-28 0 ... ... ... 0 0 0 0 0
51 7.8E-14 1.8E-21 1.9E-49 0 0 1.33E-34 ... ... ... 0 0 0 0 1.38E-15
52 7.3E-14 3.9E-05 9.8E-64 0 0 7.54E-28 ... ... ... 0 0 0 0 2.08E-07
53 0.00050 2.2E-18 1.5E-49 0 0 3.85E-37 ... ... ... 0 0 0 0 3.46E-15
54 2.4E-07 6.2E-17 1.1E-52 0 0 4.17E-50 ... ... ... 0 0 0 0 1.37E-13
55 9.0E-09 2.5E-10 1.0E-57 0 0 3.3E-33 ... ... ... 0 0 0 0 1.31E-15
56 6.1E-09 9.0E-08 7.1E-60 0 0 2.01E-24 ... ... ... 0 0 0 0 2.19E-08
57 2.3E-09 2.7E-19 4.5E-50 0 0 8.27E-38 ... ... ... 0 0 0 0 1.09E-22
58 0 0 4E-146 0 0 3.1E-282 ... ... ... 7.29E-06 8.6E-13 6.7E-138 2.4E-151 0
59 5.8E-19 5.1E-20 4.2E-47 0 0 8.98E-22 ... ... ... 0 0 0 0 4.55E-22
60 2.9E-18 7.7E-10 1.2E-58 0 0 8.78E-41 ... ... ... 0 0 0 0 5.34E-16
61 0 0 2.6E-18 0 0 8.6E-308 ... ... ... 1.86E-27 7.3E-35 1.3E-115 6.3E-117 0
62 1.3E-20 1 4.5E-68 0 0 1.53E-15 ... ... ... 0 0 0 0 1.02E-05
63 0 0 1.4E-16 0 0 9.8E-295 ... ... ... 1 0.01876 7.2E-138 5.7E-155 0
64 0 0 0 0 0 0 ... ... ... 0 0 1.05E-63 4.13E-59 0
65 3.4E-15 4.0E-09 6.0E-61 0 0 7.73E-44 ... ... ... 0 0 0 0 4.2E-10
66 7.6E-20 0.784014 2.2E-68 0 0 4.25E-17 ... ... ... 0 0 0 0 8.95E-06
67 0 1.8E-24 5.3E-60 0 0 6.6E-238 ... ... ... 2.1E-49 4.2E-53 0 0 7.5E-273
68 7.5E-27 0.00058 3.5E-64 0 0 4.52E-06 ... ... ... 0 0 0 0 2.61E-11
69 0 0 1.7E-16 0 0 0 ... ... ... 4.33E-52 7.2E-63 3.2E-177 4.1E-187 0
70 0 1.9E-25 9.0E-73 0 0 3.3E-253 ... ... ... 7.07E-40 3.0E-38 0 0 2E-292
71 6.7E-09 3.3E-05 6.9E-64 0 0 1.18E-27 ... ... ... 0 0 0 0 4.17E-05
72 0 0 4.3E-18 0 0 9.1E-307 ... ... ... 9.26E-19 1.3E-27 9.5E-105 3.5E-111 0
73 0 0 0 0 0 0 ... ... ... 7.13E-90 2.4E-10 8.49E-07 3.71E-11 0
74 1.2E-26 3.4E-05 6.9E-64 0 0 1.56E-08 ... ... ... 0 0 0 0 2.57E-11
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Data Degree of Membership (in cluster)
1 2 3 4 5 6 ... ... ... 37 38 39 40 41
75 0 0 0 0 0 0 ... ... ... 3.3E-231 3.4E-25 1.48E-25 2.74E-13 0
76 0 0 0 0 0 0 ... ... ... 0 0 1.8E-140 5E-132 0
77 2.5E-25 1.7E-05 6.4E-65 0 0 1.24E-31 ... ... ... 0 0 0 0 1.07E-14
78 0 0 2.6E-15 0 0 4.5E-297 ... ... ... 0.001876 1 3.6E-154 4.3E-173 0
79 0 0 0 0.91280 1 0 ... ... ... 0 0 0 0 0
80 0 0 0 0 0 0 ... ... ... 0 0 0 0 0
81 3.8E-08 1.1E-12 1.6E-56 0 0 1.03E-29 ... ... ... 0 0 0 0 1.06E-12
83 0 0 0 0 0 0 ... ... ... 0 0 3.68E-49 1.82E-40 0
84 0 0 0 0 0 0 ... ... ... 1.8E-240 1.1E-25 1.28E-15 1.06E-14 0
85 1.2E-12 9.5E-10 8.4E-59 0 0 6.03E-19 ... ... ... 0 0 0 0 3.42E-09
86 1.8E-12 3.4E-39 7.0E-32 0 0 1E-56 ... ... ... 0 0 0 0 1.94E-29
87 3.3E-06 5.5E-12 9.8E-58 0 0 4.51E-36 ... ... ... 0 0 0 0 1.77E-12
88 4.1E-72 1.0E-37 2.5E-28 0 0 2.1E-08 ... ... ... 7.8E-245 9.1E-24 0 0 8.86E-50
89 0 0 3.3E-26 0 0 0 ... ... ... 2.33E-28 1.4E-35 5.42E-52 4.85E-62 0
90 0 0 0 0 0 0 ... ... ... 0 0 7.01E-85 3.77E-77 0
91 1.8E-12 4.6E-11 1.8E-57 0 0 6.86E-20 ... ... ... 0 0 0 0 6.22E-12
92 5.2E-05 8.7E-19 1.3E-49 0 0 1.84E-40 ... ... ... 0 0 0 0 6.18E-22
93 0 0 0 0 0 0 ... ... ... 7.2E-138 3.6E-15 1 0.001365 0
94 3.7E-14 2.4E-09 3.3E-58 0 0 1.68E-12 ... ... ... 0 0 0 0 6.81E-11
95 1.0E-51 1.4E-18 2.8E-47 0 0 0.276625 ... ... ... 6.9E-283 1.5E-28 0 0 1.12E-25
96 0 0 0 0 0 0 ... ... ... 5.7E-155 4.3E-17 0.001365 1 0
97 0 0 3.8E-293 0 0 0 ... ... ... 4.64E-45 2.6E-51 5.87E-53 3.69E-53 0
98 2.1E-18 9.5E-06 7.3E-63 0 0 8.34E-30 ... ... ... 0 0 0 0 2.24E-13
99 0 0 0 0 0 0 ... ... ... 5.68E-80 4.1E-93 4.66E-09 5.55E-14 0
100 6.1E-11 1.4E-09 4.0E-60 0 0 7.5E-30 ... ... ... 0 0 0 0 5.35E-11
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Table Appendix 2. Fuzzy Subtractive Clustering Degree of Membership Radius 0.3
Data Degree of Membership (in cluster 1) Data Degree of Membership (in cluster 1)
1 0.007922779 42 0.007922779
2 9.45785E-06 43 9.45785E-06
3 0.141481555 44 0.141481555
4 0.310613494 45 0.310613494
5 0.119200731 46 0.119200731
6 1.98793E-57 47 1.98793E-57
7 1.46405E-07 48 1.46405E-07
8 3.0715E-08 49 3.0715E-08
9 0.054625102 50 0.054625102
10 0.069901216 51 0.069901216
11 0.397253626 52 0.397253626
12 0.141782866 53 0.141782866
13 0.060023377 54 0.060023377
14 0.035448008 55 0.035448008
15 0.020390709 56 0.020390709
16 0.244509782 57 0.244509782
17 0.334595848 58 0.334595848
18 0.297915903 59 0.297915903
19 4.06043E-66 60 4.06043E-66
20 0.000831195 61 0.000831195
21 0.313877607 62 0.313877607
22 0.052637666 63 0.052637666
23 1 64 1
24 0.561227691 65 0.561227691
25 1.18421E-60 66 1.18421E-60
26 0.168284776 67 0.168284776
27 0.580936763 68 0.580936763
28 0.298736753 69 0.298736753
29 0.527902738 70 0.527902738
30 0.000764753 71 0.000764753
31 1.80958E-15 72 1.80958E-15
32 8.06444E-55 73 8.06444E-55
33 0.082530224 74 0.082530224
34 0.061110377 75 0.061110377
35 0.061110377 76 0.061110377
36 0.578788297 77 0.578788297
37 0.212270097 78 0.212270097
38 0.1130885 79 0.1130885
39 0.244438291 80 0.244438291
40 8.07658E-27 81 8.07658E-27
41 0.405447464 82 0.405447464
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Data Degree of Membership (in cluster 1) Data Degree of Membership (in cluster 1)
83 5.0547E-119 92 0.150686482
84 1.2986E-106 93 2.6332E-85
85 0.3545226 94 0.115026844
86 0.000435418 95 0.000265094
87 0.135632956 96 3.78232E-87
88 2.60047E-06 97 2.62789E-57
89 3.55608E-55 98 0.485654125
90 6.7795E-139 99 3.65395E-72
91 0.239949452 100 0.771170984
Table Appendix 3. Fuzzy Subtractive Clustering Degree of Membership Radius 0.4
Data Degree of Membership (in cluster 1) Data Degree of Membership (in cluster 1)
1 0.065783749 31 5.09786E-09
2 0.001492394 32 3.73635E-31
3 0.332865398 33 0.245807328
4 0.518052686 34 0.207581987
5 0.302278244 35 0.207581987
6 1.27453E-32 36 0.735220071
7 0.000143095 37 0.418191268
8 5.94476E-05 38 0.293459298
9 0.194887124 39 0.452736175
10 0.223883796 40 2.10288E-15
11 0.594943436 41 0.601815274
12 0.333263967 42 0.25680225
13 0.205496883 43 0.522562581
14 0.15280776 44 1.28068E-49
15 0.111958143 45 0.218902954
16 0.452810651 46 0.477844495
17 0.540185357 47 0.14126319
18 0.506031671 48 0.209306944
19 1.64938E-37 49 0.090383389
20 0.018506867 50 6.30477E-48
21 0.521107937 51 0.045571534
22 0.190866342 52 0.840585731
23 1 53 0.145743748
24 0.72258799 54 0.4022737
25 1.95571E-34 55 0.66285148
26 0.366986607 56 0.213753666
27 0.736753969 57 0.411716711
28 0.506815478 58 2.8905E-23
29 0.698130444 59 0.08109693
30 0.017659595 60 0.268695559
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Data Degree of Membership (in cluster 1) Data Degree of Membership (in cluster 1)
61 2.95905E-25 81 0.530935088
62 0.430222369 82 0.560359821
63 3.20603E-24 83 3E-67
64 6.26542E-70 84 2.74679E-60
65 0.30802172 85 0.55805205
66 0.466216544 86 0.012864267
67 8.40306E-17 87 0.325053944
68 0.18163346 88 0.000721883
69 3.94103E-24 89 2.35734E-31
70 4.02462E-18 90 1.90567E-78
71 0.425634566 91 0.448040596
72 9.20635E-26 92 0.344879032
73 3.85854E-42 93 2.65474E-48
74 0.10809475 94 0.296278101
75 6.15592E-57 95 0.009731116
76 7.12759E-91 96 2.44056E-49
77 0.392888257 97 1.49118E-32
78 5.1385E-24 98 0.666129985
79 2.12149E-49 99 6.55472E-41
80 0 100 0.864016941
Table Appendix 4. Fuzzy Subtractive Clustering Degree of Membership Radius 0.5
Data Degree of Membership (in cluster 1) Data Degree of Membership (in cluster 1)
1 0.065783749 20 0.018506867
2 0.001492394 21 0.521107937
3 0.332865398 22 0.190866342
4 0.518052686 23 1
5 0.302278244 24 0.72258799
6 1.27453E-32 25 1.95571E-34
7 0.000143095 26 0.366986607
8 5.94476E-05 27 0.736753969
9 0.194887124 28 0.506815478
10 0.223883796 29 0.698130444
11 0.594943436 30 0.017659595
12 0.333263967 31 5.09786E-09
13 0.205496883 32 3.73635E-31
14 0.15280776 33 0.245807328
15 0.111958143 34 0.207581987
16 0.452810651 35 0.207581987
17 0.540185357 36 0.735220071
18 0.506031671 37 0.418191268
19 1.64938E-37 38 0.293459298
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Data Degree of Membership (in cluster 1) Data Degree of Membership (in cluster 1)
39 0.452736175 70 4.02462E-18
40 2.10288E-15 71 0.425634566
41 0.601815274 72 9.20635E-26
42 0.25680225 73 3.85854E-42
43 0.522562581 74 0.10809475
44 1.28068E-49 75 6.15592E-57
45 0.218902954 76 7.12759E-91
46 0.477844495 77 0.392888257
47 0.14126319 78 5.1385E-24
48 0.209306944 79 2.12149E-49
49 0.090383389 80 0
50 6.30477E-48 81 0.530935088
51 0.045571534 82 0.560359821
52 0.840585731 83 3E-67
53 0.145743748 84 2.74679E-60
54 0.4022737 85 0.55805205
55 0.66285148 86 0.012864267
56 0.213753666 87 0.325053944
57 0.411716711 88 0.000721883
58 2.8905E-23 89 2.35734E-31
59 0.08109693 90 1.90567E-78
60 0.268695559 91 0.448040596
61 2.95905E-25 92 0.344879032
62 0.430222369 93 2.65474E-48
63 3.20603E-24 94 0.296278101
64 6.26542E-70 95 0.009731116
65 0.30802172 96 2.44056E-49
66 0.466216544 97 1.49118E-32
67 8.40306E-17 98 0.666129985
68 0.18163346 99 6.55472E-41
69 3.94103E-24 100 0.864016941
Table Appendix 5. Fuzzy Subtractive Clustering Degree of Membership Radius 0.6
Data Degree of Membership (in cluster 1) Data Degree of Membership (in cluster 1)
1 0.065783749 9 0.018506867
2 0.001492394 10 0.521107937
3 0.332865398 11 0.190866342
4 0.518052686 12 1
5 0.302278244 13 0.72258799
6 1.27453E-32 14 1.95571E-34
7 0.000143095 15 0.366986607
8 5.94476E-05 16 0.736753969
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Data Degree of Membership (in cluster 1) Data Degree of Membership (in cluster 1)
17 0.194887124 59 0.506815478
18 0.223883796 60 0.698130444
19 0.594943436 61 0.017659595
20 0.333263967 62 5.09786E-09
21 0.205496883 63 3.73635E-31
22 0.15280776 64 0.245807328
23 0.111958143 65 0.207581987
24 0.452810651 66 0.207581987
25 0.540185357 67 0.735220071
26 0.506031671 68 0.418191268
27 1.64938E-37 69 0.293459298
28 0.452736175 70 4.02462E-18
29 2.10288E-15 71 0.425634566
30 0.601815274 72 9.20635E-26
31 0.25680225 73 3.85854E-42
32 0.522562581 74 0.10809475
33 1.28068E-49 75 6.15592E-57
34 0.218902954 76 7.12759E-91
35 0.477844495 77 0.392888257
36 0.14126319 78 5.1385E-24
37 0.209306944 79 2.12149E-49
38 0.090383389 80 0
39 6.30477E-48 81 0.530935088
40 0.045571534 82 0.560359821
41 0.840585731 83 3E-67
42 0.145743748 84 2.74679E-60
43 0.4022737 85 0.55805205
44 0.66285148 86 0.012864267
45 0.213753666 87 0.325053944
46 0.411716711 88 0.000721883
47 2.8905E-23 89 2.35734E-31
48 0.08109693 90 1.90567E-78
49 0.268695559 91 0.448040596
50 2.95905E-25 92 0.344879032
51 0.430222369 93 2.65474E-48
52 3.20603E-24 94 0.296278101
53 6.26542E-70 95 0.009731116
54 0.30802172 96 2.44056E-49
55 0.466216544 97 1.49118E-32
56 8.40306E-17 98 0.666129985
57 0.18163346 99 6.55472E-41
58 3.94103E-24 100 0.864016941
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Table Appendix 6. Fuzzy Subtractive Clustering Degree of Membership Radius 0.7
Data Degree of Membership (in cluster 1) Data Degree of Membership (in cluster 1)
1 0.411225037 42 0.641528483
2 0.119450069 43 0.809027956
3 0.698242196 44 1.08413E-16
4 0.8067414 45 0.608936432
5 0.676607713 46 0.785737088
6 3.84964E-11 47 0.527786713
7 0.055551275 48 0.600088169
8 0.041698986 49 0.456174472
9 0.586262959 50 3.86943E-16
10 0.613426456 51 0.364772775
11 0.844032957 52 0.944873608
12 0.698515088 53 0.533195541
13 0.596499211 54 0.742786854
14 0.54150005 55 0.874353257
15 0.489201264 56 0.60422163
16 0.772051459 57 0.748435899
17 0.817837536 58 4.36835E-08
18 0.800580418 59 0.440307967
19 9.7573E-13 60 0.651082583
20 0.271788549 61 9.78544E-09
21 0.808291896 62 0.759258298
22 0.582285686 63 2.13049E-08
23 1 64 2.5298E-23
24 0.899339164 65 0.680779003
25 9.8419E-12 66 0.779441872
26 0.720850109 67 5.63426E-06
27 0.905058663 68 0.57293423
28 0.800985118 69 2.27903E-08
29 0.889284075 70 2.08886E-06
30 0.267661278 71 0.756604968
31 0.001959784 72 6.68356E-09
32 1.16004E-10 73 3.00054E-14
33 0.632427222 74 0.483623755
34 0.598468813 75 4.42062E-19
35 0.598468813 76 3.66628E-30
36 0.904442948 77 0.73708305
37 0.752258899 78 2.48528E-08
38 0.670097629 79 1.27838E-16
39 0.772009992 80 4.00098E-94
40 1.61232E-05 81 0.813237898
41 0.847203977 82 0.827688215
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Data Degree of Membership (in cluster 1) Data Degree of Membership (in cluster 1)
83 1.87114E-22 92 0.70637294
84 3.56003E-20 93 2.91734E-16
85 0.826573614 94 0.672192607
86 0.241355024 95 0.220329944
87 0.692848867 96 1.33822E-16
88 0.094230876 97 4.05213E-11
89 9.98063E-11 98 0.875763028
90 4.18848E-26 99 7.56615E-14
91 0.769386295 100 0.95339435
Table Appendix 7. Fuzzy Subtractive Clustering Degree of Membership Radius 0.8
Data Degree of Membership (in cluster 1) Data Degree of Membership (in cluster 1)
1 0.506441929 31 0.008449811
2 0.196549001 32 2.47236E-08
3 0.75956888 33 0.704123285
4 0.848385979 34 0.674990121
5 0.741483895 35 0.674990121
6 1.06252E-08 36 0.925985825
7 0.109372053 37 0.804162357
8 0.087807898 38 0.736015514
9 0.664424727 39 0.820278445
10 0.687868886 40 0.000214143
11 0.878251539 41 0.880776668
12 0.759796153 42 0.711868386
13 0.673288675 43 0.850226382
14 0.625225025 44 5.98219E-13
15 0.578447464 45 0.684010716
16 0.820312177 46 0.831422258
17 0.857305682 47 0.61306603
18 0.843421028 48 0.676388023
19 6.3728E-10 49 0.548304936
20 0.368835936 50 1.58459E-12
21 0.849634075 51 0.462033444
22 0.660970897 52 0.957514817
23 1 53 0.617870532
24 0.921982514 54 0.796398457
25 3.73961E-09 55 0.902306441
26 0.77832782 56 0.679952215
27 0.926468421 57 0.801031554
28 0.843747438 58 2.31869E-06
29 0.914079869 59 0.533643353
30 0.364539996 60 0.719971196
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Data Degree of Membership (in cluster 1) Data Degree of Membership (in cluster 1)
61 7.37544E-07 81 0.853611696
62 0.809884798 82 0.865200471
63 1.33811E-06 83 2.31517E-17
64 5.00308E-18 84 1.28738E-15
65 0.744981238 85 0.864308287
66 0.826317442 86 0.336779977
67 9.57435E-05 87 0.755072859
68 0.652828287 88 0.163914242
69 1.40897E-06 89 2.20346E-08
70 4.479E-05 90 3.71545E-20
71 0.807716998 91 0.818143231
72 5.50835E-07 92 0.766331535
73 4.43206E-11 93 1.27645E-12
74 0.573391367 94 0.73777662
75 8.85775E-15 95 0.314080278
76 2.9056E-23 96 7.02866E-13
77 0.791712063 97 1.10505E-08
78 1.5056E-06 98 0.903420094
79 6.78673E-13 99 8.99784E-11
80 3.10659E-72 100 0.964118829
Table Appendix 8. Fuzzy Subtractive Clustering Degree of Membership Radius 0.9
Data Degree of Membership (in cluster 1) Data Degree of Membership (in cluster 1)
1 0.746080464 20 0.70730003
2 0.309353434 21 0.80182171
3 0.869515906 22 0.760786183
4 0.843924803 23 0.885460005
5 0.753978059 24 0.911078536
6 1.47979E-06 25 1.79715E-06
7 0.345197495 26 0.705377501
8 0.281401572 27 0.937115098
9 0.61108692 28 0.703890507
10 0.888537084 29 0.812934484
11 0.852298054 30 0.6381877
12 0.699959022 31 0.037168592
13 0.552663182 32 6.38246E-06
14 0.544301301 33 0.743187474
15 0.777567856 34 0.665584223
16 0.812642688 35 0.665584223
17 1 36 0.80097415
18 0.754729096 37 0.891317544
19 4.63586E-07 38 0.726496266
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Data Degree of Membership (in cluster 1) Data Degree of Membership (in cluster 1)
39 0.801380931 70 0.000412058
40 0.000941636 71 0.894625526
41 0.702590183 72 2.43404E-05
42 0.660638663 73 2.94088E-08
43 0.82868471 74 0.87238262
44 1.11375E-09 75 5.2048E-11
45 0.744580429 76 2.5646E-17
46 0.829296813 77 0.783942914
47 0.746142375 78 4.60134E-05
48 0.646504466 79 1.2152E-09
49 0.850883468 80 5.59979E-60
50 5.59079E-09 81 0.804330587
51 0.649208652 82 0.948480812
52 0.88438474 83 6.39964E-13
53 0.719805884 84 1.33917E-11
54 0.678368995 85 0.890646756
55 0.822706707 86 0.436200244
56 0.864278568 87 0.786239775
57 0.703816692 88 0.40441887
58 6.58436E-05 89 2.54732E-06
59 0.688009758 90 5.37208E-15
60 0.724011199 91 0.874616388
61 2.72423E-05 92 0.70329804
62 0.955670933 93 2.18754E-09
63 4.42437E-05 94 0.909084684
64 1.79402E-13 95 0.645905124
65 0.731431971 96 1.3776E-09
66 0.949703226 97 1.42519E-06
67 0.000686236 98 0.839757391
68 0.924393965 99 4.90883E-08
69 3.5449E-05 100 0.851557602
Table Appendix 9. Fuzzy Subtractive Clustering Degree of Membership Radius 1
Data Degree of Membership (in cluster 1) Data Degree of Membership (in cluster 1)
1 0.78878091 9 0.671032292
2 0.386605922 10 0.908713965
3 0.892924625 11 0.878575548
4 0.871577556 12 0.749046568
5 0.795537312 13 0.618575952
6 1.89611E-05 14 0.610984076
7 0.422507853 15 0.815639073
8 0.358058906 16 0.845315246
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Data Degree of Membership (in cluster 1) Data Degree of Membership (in cluster 1)
17 1 59 0.738671978
18 0.796179123 60 0.769827959
19 7.40569E-06 61 0.0002007
20 0.755403474 62 0.963939518
21 0.83618626 63 0.000297262
22 0.801350882 64 4.73806E-11
23 0.906164093 65 0.776212963
24 0.927342599 66 0.959060954
25 2.21929E-05 67 0.002738695
26 0.753739887 68 0.938305479
27 0.948751067 69 0.000248416
28 0.752452583 70 0.001811824
29 0.845561095 71 0.913754316
30 0.695037485 72 0.0001832
31 0.069477255 73 7.93354E-07
32 6.19499E-05 74 0.895308431
33 0.786302559 75 4.68044E-09
34 0.719108538 76 3.64171E-14
35 0.719108538 77 0.821051494
36 0.835470241 78 0.000306857
37 0.911016596 79 6.00571E-08
38 0.771967546 80 1.01396E-48
39 0.835813907 81 0.838304917
40 0.003538714 82 0.95806092
41 0.751326458 83 1.32735E-10
42 0.714777427 84 1.55861E-09
43 0.858806561 85 0.910461209
44 5.59627E-08 86 0.510676158
45 0.787496096 87 0.822999475
46 0.859320351 88 0.480323066
47 0.788833927 89 2.94393E-05
48 0.702365124 90 2.76322E-12
49 0.877394221 91 0.89716488
50 2.06754E-07 92 0.751939535
51 0.70474383 93 9.66862E-08
52 0.90527266 94 0.925698406
53 0.766204094 95 0.701837664
54 0.730276713 96 6.648E-08
55 0.853784922 97 1.83923E-05
56 0.888565675 98 0.868089706
57 0.752388668 99 1.20141E-06
58 0.0004102 100 0.87795724
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